Term
What does this denote?
[image]
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Definition
n choose k.
The number of combinations of n objects taken k at a time.
The equation is:
n!/[k!(n-k)!] |
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Term
What does this denote?
[image]
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Definition
n choose k.
The number of combinations of n objects taken k at a time.
The equation is:
n!/[k!(n-k)!] |
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Term
| In Data Analysis, What is a Variable? |
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Definition
| Any characteristic that can vary for the population of individuals or objects being analyzed. |
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Term
| Fill in the Blank: Gender and age both represent ______ among people. |
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Definition
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Term
| How Many Variables are Observed Simultaneously When Collecting Data from a Population? |
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Definition
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Term
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Definition
| The values of a variable and how frequently the values are observed in the data. |
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Term
| Distribution of a Variable |
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Definition
| The values of that variable and how frequently the values are observed in the data. |
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Term
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Definition
| The number of times that a particular category or numerical value appears in the data. |
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Term
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Definition
| The number of times that a particular category or numerical value appears in the data. |
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Term
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Definition
| A table or graph that represents the categories or numerical values along with their associated frequencies. |
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Term
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Definition
| The frequency of a category or numerical value divided by the total number of data. |
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Term
| How can Relative Frequencies be Expressed? |
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Definition
| In terms of percents, fractions, or decimals. |
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Term
| Relative Frequency Distribution |
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Definition
A table or graph that presents the relative frequencies of the categories or numerical values.
The total of the relative frequencies is 100% if percentages are used, and 1 if fractions or decimals are used. |
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Term
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Definition
A graphical display for representing frequencies where rectangular bars represent the categories of the data and the height of each bar is proportional to the corresponding frequency (or relative frequency).
They can also be used to compare different groups using the same categories. |
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Term
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Definition
A graphical display for representing frequencies where rectangular bars represent the categories of the data and the height of each bar is proportional to the corresponding frequency (or relative frequency).
They can also be used to compare different groups using the same categories. |
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Term
| Are the Bars in a Bar Graph Presented Vertically or Horizontally? |
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Definition
| They can be represented in either way. |
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Term
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Definition
A bar graph which is used to show how different subgroups or subcategories contribute to an entire group or category.
Each bar represents a category that consists of more than one subcategory.
Each bar is divided into segments which represent the different subcategories, where the height of each segment represents the frequency or relative frequency of the subcategory that the segment represents. |
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Term
| Fill in the Blank: The Height of the Segment of a Bar in a Segmented Bar Graph Represents the Frequency or Relative Frequency of a Particular ______. |
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Definition
| Subcategory (or subgroup). |
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Term
| Fill in the Blank: The Height of the Segment of a Bar in a Segmented Bar Graph Represents the ______ of a Particular Subcategory. |
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Definition
| Frequency or relative frequency. |
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Term
| Can a Bar Graph be Used to Compare Something Other than Frequencies or Relative Frequencies? |
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Definition
| Yes. They can be used to compare numerical data, such as temperatures, dollar amounts, and ages. |
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Term
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Definition
A graphical display for representing how a whole is separated into parts.
The area of the circle graph representing each category is proportional to the part of the whole that the category represents. |
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Term
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Definition
A graphical display for representing how a whole is separated into parts.
The area of the circle graph representing each category is proportional to the part of the whole that the category represents. |
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Term
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Definition
The part of a circle graph which represents a particular category.
The measure of the central angle of a sector is proportional to the percent of 360ᵒ that the sector represents. |
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Term
| If the Sector Representing a Category is 15% of the Total, What Will be the Measure of the Sector? |
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Definition
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Term
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Definition
Values which are grouped into intervals, usually used when a list of data is large and contains many different values of numerical variables.
In a class, each interval has a frequency and a relative frequency. |
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Term
| How Do You Group Data into Classes? |
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Definition
| Divide the entire intervale of values into smaller intervals of equal length, then count the values that fall into each interval. |
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Term
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Definition
A graphical display for representing classes, similar to bar graphs except that they have a number line for the horizontal axis and there are no spaces between the bars.
They are useful for identifying the general shape of a distribution of data. |
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Term
| Fill in the Blank: The Spaces Between Bars in a Histogram Indicate that There are ______ in Those Intervals. |
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Definition
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Term
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Definition
| Data resulting from observing a single characteristic or variable. |
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Term
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Definition
| Data resulting from observing two different characteristics or variables in the same population of individuals or objects. |
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Term
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Definition
A graphical display for representing data when there are two variables being analyzed simultaneously.
The values of one variable appear on the horizontal axis and the values of the other appear on the vertical axis.
Each point in a scatterplot represents a single individual or object in the data.
In many cases, a line or curve that best represents the trend is also displayed and used to make predictions. |
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Term
| Fill in the Blank: In a Scatterplot, Each Individual is Represented by a ______ in the Coordinate System. |
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Definition
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Term
| Fill in the Blanks: In a Scatterplot, One Variable Appears on the ______ and the Other Appears on the ______. |
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Definition
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Term
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Definition
| The overall pattern in the relationship between two variables. |
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Term
| Fill in the Blanks: In a Scatterplot, the ______ of the Trend as well as ______ from the Trend are Evident. |
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Definition
| Strength, striking deviations. |
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Term
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Definition
The line or curve that best represents the data of a trend.
How scattered or close the data are to the trend line shows how well the trend line fits the data. |
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Term
| Fill in the Blank: In Many Cases, a ______ that Best Represents the Trend of the Scatterplot Will Also be Displayed and Used to Make Predictions About the Population or Objects. |
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Definition
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Term
| If You Wanted to Know How a Change in One Variable Affected the Other, How Would You Use the Trend Line? |
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Definition
| You would use the trend line to determine the slope of the data between two points (with the desired value on top and the known on the bottom), then multiply that slope by the known change. |
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Term
| If One Point on the Trend Line Was at (2.5,7) and Another Was at (0,2), What Would You Expect the Change in the Second Value to be If The First Value Increased by 3? |
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Definition
First determine the slope:
[(2)-(7)]/[(0)-(2.5)]
-5/-2.5
5/2.5
Then multiply the slope by the change of the first value:
(3)(5/2.5)
15/2.5
Which is equivalent to 6. |
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Term
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Definition
A graphical display useful for showing changes in data collected at regular intervals of time.
The time is always on the horizontal axis and the variable is always on the vertical axis.
Consecutive observations are connected by a line segment to emphasize the increase or decrease over time. |
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Term
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Definition
A graphical display useful for showing changes in data collected at regular intervals of time.
The time is always on the horizontal axis and the variable is always on the vertical axis.
Consecutive observations are connected by a line segment to emphasize the increase or decrease over time. |
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Term
| Fill in the Blank: In a Time Plot, the Time is Always Represented on the ______. |
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Definition
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Term
| Fill in the Blank: In a Time Plot, the Variable is Always Represented on the ______. |
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Definition
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Term
| What Can Time Plots be Used to Compare? |
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Definition
| Frequencies or numerical data (such as temperatures, dollar amounts, percents, and ages). |
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Term
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Definition
| Numerical descriptions of data, often grouped into three categories: measures of central tendency, measures of position, and measures of dispersion. |
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Term
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Definition
| Numerical descriptions of data, often grouped into three categories: measures of central tendency, measures of position, and measures of dispersion. |
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Term
| Measures of Central Tendency |
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Definition
The 'center' of the data along the number line, usually reported as values that represent the data.
The three common measures are mean, median, and mode. |
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Term
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Definition
| A way of determining the center (or statistical average) of the data, determined by adding up the values, then dividing by the number of values. |
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Term
| How Do You Calculate the Mean? |
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Definition
Take the sum of n numbers and divide it by n.
Where n is the number of data.
For example, if your data is: 1,6,8,9,3,5,1,6
You can see that there are 8 numbers.
Therefore, you would calculate the mean by: (1+6+8+9+3+5+1+6)/8
The mean in this case is 4.875. |
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Term
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Definition
The mean used in statistics, where a number apppears in the calculation the same number of times it appears in the data.
This is the mean generally used on the GRE.
It can be thought of as the balance point, because it balances all of the values. |
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Term
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Definition
The number of times a value appears in the list, or the frequency of that value.
The sum of the weights is the number of numbers in the list. |
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Term
| Fill in the Blank: The Sum of the Weights is Equal to the Number of ______. |
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Definition
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Term
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Definition
A way of determining the center (or statistical average) of the data, which is a measure of the central tendency.
It can be thought of as the halving point, because it divides the data into two groups (high and low) with an equal number of points (or number of values) in each group. |
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Term
| Fill in the Blank: The Median is ______ by Unusually High or Low Values Relative to the Rest of the Data. |
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Definition
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Term
| How Do You Calculate the Median? |
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Definition
Order the numbers (data) from least to greatest.
If there are an odd number of points, the median will be the middle number in the list.
If there are an even number of points, the median will be the average of the two middle numbers in the list. |
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Term
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Definition
| A way of determining the center (or statistical average) of the data, it will be the number that occurs most frequently in the list. |
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Term
| How Do You Calculate the Mode? |
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Definition
| Determine which number occurs most frequently in the list. That number is the mode. |
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Term
| Calculate the Mean for: 13,18,13,14,13,16,14,21,13 |
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Definition
There are nine values, so the mean will be the sum of the values divided by 9.
(13+18+13+14+13+16+14+21+13)/9
135/9
15
So the answer is 15. |
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Term
| Calculate the Median for: 13,18,13,14,13,16,14,21,13 |
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Definition
First, we have to rewrite the list in order: 13,13,13,13,14,14,16,18,21
There are 9 values in the list, which is an odd number, so the median will be the central number.
If we had a large number of values, it might be helpful to use the following equation to figure out which item will be the central number: C = (n+1)/2.
In this case, the central number is the 5th number, which would be 14.
So the answer is 14. |
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Term
| Calculate the Median for: 13,18,13,14,13,16,14,21,13,12 |
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Definition
First, we have to rewrite the list in order: 12,13,13,13,13,14,14,16,18,21
There are 10 values in the list, which is an even number, so the median will be the average of the two central numbers.
If we had a large number of values, it might be helpful to use the following equation to figure out which items will be the central numbers: C = (n+1)/2 (in this case, you would take two numbers closest to the result and average them).
In this case, the central numbers are the 5th and 6th numbers, which would be 13 and 14.
So the answer is (13+14)/2, or 13.5. |
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Term
| Calculate the Mode for: 13,18,13,14,13,16,14,21,13 |
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Definition
First, we have to rewrite the list so that like numbers are grouped together: 13,13,13,13,14,14,16,18,21
Then, we determine the weights of each number: 4(13),2(14),1(16),1(18),1(21)
The answer is the number with the highest weight.
So the answer is 13.
There are other ways to calculate this. As long as the answer you get is always the one that is repeated most often in the list, you should use the method that works best for you. |
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Term
| Most Basic Positions in a List of Data |
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Definition
| The least, the greatest, and the middle (median). Usually represented as L, G, and M. |
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Term
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Definition
| A common measure of position, there are three of these numbers, which divide the data into four groups. |
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Term
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Definition
| A common measure of position, there are 99 of these numbers, which divide the data into 100 groups. |
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Term
| How Do You Calculate the First Quartile? |
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Definition
It will be the average of the median and the least (smallest) number on the list.
L+M/2 |
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Term
| How Do You Calculate the Second Quartile? |
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Definition
It is the same as the median, so you need to order the numbers (data) from least to greatest.
If there are an odd number of points, it will be the middle number in the list.
If there are an even number of points, it will be the average of the two middle numbers in the list. |
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Term
| How Do You Calculate the Third Quartile? |
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Definition
It will be the average of the median and the greatest (largest) number on the list.
G+M/2 |
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Term
| What is the Denotation for the Different Quartiles? |
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Definition
| Q₁ is the first, Q₂ is the second, and Q₃ is the third. |
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Term
| Find Q₁ for: 13,18,13,14,13,16,14,21,13 |
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Definition
First, we have to rewrite the list in order: 13,13,13,13,14,14,16,18,21
Next, we have to determine the median, M, or central number. In this case, it is 14.
Then we find the least number, L. It will be the first number on the ordered list, in this case 13.
Finally, we plug L and M into the equation: L+M/2
[(13)+(14)]/2 = 13.5
So the answer is 13.5. |
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Term
| Find Q₂ for: 13,18,13,14,13,16,14,21,13 |
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Definition
First, we have to rewrite the list in order: 13,13,13,13,14,14,16,18,21
There are 9 values in the list, which is an odd number, so it will be the central number.
If we had a large number of values, it might be helpful to use the following equation to figure out which item will be the central number: C = (n+1)/2.
In this case, the central number is the 5th number, which would be 14.
So the answer is 14. |
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Term
| Find Q₃ for: 13,18,13,14,13,16,14,21,13 |
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Definition
First, we have to rewrite the list in order: 13,13,13,13,14,14,16,18,21
Next, we have to determine the median, M, or central number. In this case, it is 14.
Then we find the greatest number, G. It will be the last number on the ordered list, in this case 21.
Finally, we plug G and M into the equation: G+M/2
[(21)+(14)]/2 = 17.5
So the answer is 17.5. |
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Term
| If You are Asked to Calculate All Three Quartiles, Which One Should You Calculate First? |
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Definition
| You should calculate Q₂ first, since it is the same as the median, which is used to find the values of the other two quartiles. |
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Term
| If You Know the Quartiles, What Do You Know About the Percentiles? |
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Definition
You know the 25th, 50th, and 75th.
Q₁ = P₂₅
Q₂ = P₅₀
Q₃ = P₇₅ |
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Term
| If You Know the Percentiles, How Would You Determine the Quartiles? |
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Definition
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Term
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Definition
| The spread of the data, calculated using the range, the interquartile range, or the standard deviation. |
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Term
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Definition
A way of calculating the spread of the data, based on the distance between the greatest number, G, and the least number, L, in the data.
R = G-L |
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Term
| Find the Range for: 13,18,13,14,13,16,14,21,13 |
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Definition
First, we have to rewrite the list in order: 13,13,13,13,14,14,16,18,21
Then we find the least number, which is the first number on the list, in this case 13.
Then we find the greatest number, which is the last number on the list, in this case 21.
Then we plug L and G into the equation: R = G-L
R = 21-13 = 8
So the answer is 8. |
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Term
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Definition
| Data which lie so far outside the rest of the data that they are often ignored when analyzing that data. |
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Term
| Fill in the Blank: The Range is ______ by Outliers. |
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Definition
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Term
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Definition
A way of calculating the spread of the data, based on the difference between Q₁ and Q₃.
IR = Q₃-Q₁ |
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Term
| Find the Interquartile Range for: 13,18,13,14,13,16,14,21,13 |
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Definition
First, we have to rewrite the list in order: 13,13,13,13,14,14,16,18,21
Next, we have to determine the median, M, or central number. In this case, it is 14.
Then we find the least number, L. In this case, it is 13.
This allows us to calculate Q₁ using L+M/2: [(13)+(14)]/2 = 13.5
Now we find the greatest number, G. In this case, it is 21.
This allows us to calculate Q₃ using G+M/2: [(21)+(14)]/2 = 17.5
Finally, we plug Q₁ and Q₃ into the equation: IR = Q₃-Q₁
IR = (17.5)-(13.5) = 4
So the answer is 4. |
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Term
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Definition
A graphical way of displaying the center and spread of the data along a number line, using L, Q₁, Q₂, Q₃, and G.
A box is used to identify the two middle groups of data, and the lines extend outward from that box to vertical lines which indicate the least and greatest values.
They are particularly useful for comparing sets of data side by side. |
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Term
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Definition
A graphical way of displaying the center and spread of the data along a number line, using L, Q₁, Q₂, Q₃, and G.
A box is used to identify the two middle groups of data, and the lines extend outward from that box to vertical lines which indicate the least and greatest values.
They are particularly useful for comparing sets of data side by side. |
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Term
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Definition
A measure of the spread of data that depends on each number in the list. It takes into account how much each value differs from the mean, then takes a type of average from these differences.
It will be greater if the data are more spread away from the mean, and lesser if the data are more clustered around the mean.
In any group of data, most of the data are within about 3 standard deviations above or below the mean. |
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Term
| Population Standard Deviation |
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Definition
| A standard deviation in which the average is computed by using the number of items in the list. |
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Term
| Sample Standard Deviation |
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Definition
| A standard deviation in which the average is computed by using the number of items in the list minus one. |
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Term
| Fill in the Blank: The More the Data are Spread Away From the Mean, the ______ the Standard Deviation. |
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Definition
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Term
| Fill in the Blank: The More the Data are Clustered Around the Mean, the ______ the Standard Deviation. |
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Definition
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Term
| How Do you Calculate the Population Standard Deviation? |
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Definition
1) Calculate the mean.
2) Find the difference between the mean and each of the values.
3) Square each of those differences.
4) Use the number of items in the list to find the average of the squared differences.
5) Take the positive (nonnegative) square root of that average. |
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Term
| How Do you Calculate the Sample Standard Deviation? |
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Definition
1) Calculate the mean.
2) Find the difference between the mean and each of the values.
3) Square each of those differences.
4) Use the number of items in the list minus one to find the average of the squared differences.
5) Take the positive (nonnegative) square root of that average. |
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Term
| Find the Population Standard Deviation for: 13,18,13,14,13,16,14,21,13 |
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Definition
First, we have to calculate the mean. Since there are nine values, we use: (13+18+13+14+13+16+14+21+13)/9 = 135/9 = 15.
So the mean is 15.
Next we have to find the differences between the mean and each of the values, and square those differences:
(15-13)²,(15-18)²,(15-13)²,(15-14)²,(15-13)²,(15-16)²,(15-14)²,(15-21)²,(15-13)²
Then we have to divide the sum of the squared differences by the number of items in the list:
[(15-13)²+(15-18)²+(15-13)²+(15-14)²+(15-13)²+(15-16)²+(15-14)²+(15-21)²+(15-13)²]/(9)
[(2)²+(-3)²+(2)²+(1)²+(2)²+(-1)²+(1)²+(-6)²+(2)²]/9
[4+9+4+1+4+1+1+36+4]/9
64/9
So the average of the squared differences is 64/9 or approximately 7.1111.
Finally, we take the positive square root of that average:
√(64/9) = (√64)/(√9) = 8/3
So the answer is 8/3, or approximately 2.6667. |
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Term
| Find the Sample Standard Deviation for: 13,18,13,14,13,16,14,21,13 |
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Definition
First, we have to calculate the mean. Since there are nine values, we use: (13+18+13+14+13+16+14+21+13)/9 = 135/9 = 15.
So the mean is 15.
Next we have to find the differences between the mean and each of the values, and square those differences:
(15-13)²,(15-18)²,(15-13)²,(15-14)²,(15-13)²,(15-16)²,(15-14)²,(15-21)²,(15-13)²
Then we have to divide the sum of the squared differences by the number of items in the list minus one:
[(15-13)²+(15-18)²+(15-13)²+(15-14)²+(15-13)²+(15-16)²+(15-14)²+(15-21)²+(15-13)²]/(9-1)
[(2)²+(-3)²+(2)²+(1)²+(2)²+(-1)²+(1)²+(-6)²+(2)²]/8
[4+9+4+1+4+1+1+36+4]/8
64/8
So the average of the squared differences is 64/8 or 8.0.
Finally, we take the positive square root of that average:
√(64/8) = (√64)/(√8) = 8/√8
Since we know that a/√a = √a, we know that the value of 8/√8 will be √8
So the answer is √8, or approximately 2.8284. |
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Term
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Definition
The process of subtracting the mean from each value and then dividing the result by the standard deviation.
In any group of data, most of the data are within about 3 standard deviations above or below the mean. |
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Term
| How Do You Calculate the Value of n Standard Deviations Above the Mean? |
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Definition
Add the mean to the product of n and the standard deviation.
The formula used is V = M+nd, where d is the standard deviation. |
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Term
| How Do You Calculate the Value of n Standard Deviations Below the Mean? |
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Definition
Subtract the product of n and the standard deviation from the mean.
The formula used is V = nd-M, where d is the standard deviation. |
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Term
| In Any Group of Data, Most of the Data are Within About ______ Standard Deviations Above or Below the Mean. |
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Definition
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Term
| If the Standard Deviation is 2.54 and the Mean is 16, What is the Value of 3 Standard Deviations Above the Mean? |
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Definition
V = (16)+(3)(2.54)
V = 16+7.62
V = 23.62 |
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Term
| If the Standard Deviation is 2.54 and the Mean is 16, How Many Standard Deviations Below the Mean is 12? |
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Definition
We know that V = nd-M, so:
12 = n(2.54)-16
Subtract 16 from both sides: 12+16 = n(2.54)
Divide both sides by 2.54: 28/(2.54) = n
n = 28/2.54
So 12 is 28/2.54 standard deviations below the mean, or approxiately 11.02 standard deviations below the mean. |
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Term
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Definition
A collection of objects that have some property.
Some examples are: the collection of all positive integers, all points in a circular region, and all students in a school that have studied French.
Repeated elements do not matter.
The order of the elements does not matter. |
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Term
|
Definition
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Term
|
Definition
|
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Term
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Definition
A set whose members can be completely counted.
They can be listed by separating each member with a comma and using curly brackets to contain them, like this: {a, b, c, d}
One example of a finite set is the set of all philosophy majors at SJSU. |
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Term
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Definition
A set whose members cannot be completely counted.
They can not be listed, since the list would never be completed.
One example of an infinite set is the set of all positive integers. |
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Term
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Definition
| A set which has no members. It is denoted by the symbol ∅. |
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Term
| What Does the Symbol ∅ Represent? |
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Definition
|
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Term
|
Definition
| A set with one or more members. |
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Term
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Definition
A set in which all of the members are also included in another set.
For example, {2,4} is a subset of {1,2,3,4}
Every set contains a subset which is empty, denoted by ∅. |
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Term
| Fill in the Blank: ______ is a Subset of Every Set. |
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Definition
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Term
|
Definition
A collection of objects that have some property, ordered in a particular way.
It can include elements which are repeated, and those repetitions matter.
The order of a list also matters. |
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Term
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Definition
| The objects of a list. They can be repeated, and each repetition counts as a different element. |
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Term
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Definition
| The first object in a list. |
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Term
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Definition
| The second object in a list. |
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