Download 5.16 Study Guide

5.16 Study Guide
Statistics
Learning Goals
5.16
a)
b)
c)
d)
describe mean, median, and mode as measures of center;
describe mean as fair share;
find the mean, median, mode, and range of a set of data; and
describe the range of a set of data as a measure of variation.
Vocabulary
Mean – The sum of the values in a data set divided by the number of values. Also known as “average”.
Median – The middle value or the average of the two middle values in an ordered set.
Mode – The value in a data set that occurs most often.
Range – The difference between the greatest and least values in a set of data.
Skills and Strategies
The mean is computed by adding all of the numbers in the data together and dividing by the number
elements contained in the data set. [Mean represents a fair share concept of the data.]
Example :
Data Set = 2, 5, 9, 3, 5, 4, 7
Number of Elements in Data Set = 7
Mean = ( 2 + 5 + 9 + 7 + 5 + 4 + 3 ) / 7 = 5
The median of a data set is dependant on whether the number of elements in the data set is odd or
even. First reorder the data set from the smallest to the largest then if the number of elements are
odd, then the Median is the element in the middle of the data set. If the number of elements are even,
then the Median is the average of the two middle terms.
Example : Odd Number of Elements
Data Set = 2, 5, 9, 3, 5, 4, 7
Reordered = 2, 3, 4, 5, 5, 7, 9
Median = 5
Example : Even Number of Elements
Data Set = 2, 5, 9, 3, 5, 4
Reordered = 2, 3, 4, 5, 5, 9
Median = ( 4 + 5 ) / 2 = 4.5
The mode for a data set is the element that occurs the most often. It is not uncommon for a data set to
have more than one mode. This happens when two or more elements accur with equal frequency
in the data set. A data set with two modes is called bimodal. A data set with three modes is called
trimodal.
Example : Single Mode
Data Set = 2, 5, 9, 3, 5, 4, 7
Mode = 5
Example : Bimodal
Data Set = 2, 5, 2, 3, 5, 4, 7
Modes = 2 and 5
Example : Trimodal
Data Set = 2, 5, 2, 7, 5, 4, 7
Modes = 2, 5, and 7
The range for a data set is the difference between the largest value and smallest value contained in the
data set. First reorder the data set from smallest to largest then subtract the first element from the last
element.
Example :
Data Set = 2, 5, 9, 3, 5, 4, 7
Reordered = 2, 3, 4, 5, 5, 7, 9
Range = ( 9 - 2 ) = 7
Math-Aids.Com
Sample Questions
1. What is the mean (average) for the following set of data?
6, 4, 22, 21, 37
A
B
C
D
18
20
24
31
2. What is the mode for the following set of numbers?
6, 10, 8, 7, 9, 8, 9, 9, 7
A
B
C
D
6
7
8
9
3. What is the range for the following set of numbers?
21, 12, 13, 12, 24, 11, 19, 20
A
B
C
D
11
12
13
24
4. What is the median for the following set of numbers?
6, 10, 9, 4, 8, 7
A
B
C
D
7
7.5
8
8.5
5. Use the stem-and-leaf plot below to determine the mode for the following data.
Books Checked Out From the Library
Key: 1|2 = 12
A
B
C
D
12
22
24
32