#### Solved Examples and Worksheet for Measures of Central Tendency

Q1The test scores of a student in 6 subjects are 82, 95, 73, 97, 70, and 93. Find the student's average test score.
A. 83
B. 86
C. 85
D. 84

Step: 1
Average test score = Sum of all the test scoresNumber of subjects
Step: 2
Sum of the test scores of the student = 82 + 95 + 73 + 97 + 70 + 93 = 510
Step: 3
Total number of subjects is 6.
Step: 4
So, Average test score = 5106 = 85.
[Simplify.]
Q2Find the mean weight of the data set shown.
9 lb, 31 lb, 14 lb, 11 lb, 49 lb, 34 lb, 15 lb, 5 lb

A. 23 lb
B. 20 lb
C. 22 lb
D. 21 lb

Step: 1
Mean weight = Sum of the weightsNumber of listed weights
Step: 2
Sum of the weights = 9 + 31 + 14 + 11 + 49 + 34 + 15 + 5
Step: 3
= 168 lb
Step: 4
Number of listed weights = 8
Step: 5
Mean weight = 1688 = 21 lb
[Substitute and simplify.]
Step: 6
So, the mean weight of the data set is 21 lb.
Correct Answer is :   21 lb
Q3Ethan scored 24, 16, 24, 26, and 20 points in 5 games. What was his average score?

A. 25
B. 17
C. 24
D. 22

Step: 1
Average score = total scorenumber of games
[Formula for average.]
Step: 2
= 24 + 16 + 24 + 26 + 205
[Substitute the values.]
Step: 3
= 1105
[Add the values in the numerator.]
Step: 4
= 22
[Divide.]
Step: 5
So, Ethan's average score was 22.
Q4The table shows the time Lauren spends exercising in a week. Find the mean time she spends exercising.
 Day Exercise time (in minutes) Monday 26 Tuesday 18 Wednesday 28 Thursday 14 Friday 11 Saturday 23 Sunday 41

A. 23
B. 21
C. 22
D. 25

Step: 1
Mean time = Sum of all times Number of days
Step: 2
= 26+28+14+18+23+11+417
[Substitute the values given in the table.]
Step: 3
= 1617
[Add the values in the numerator.]
Step: 4
= 23
[Divide.]
Step: 5
So, Lauren spent a mean time of 23 minutes daily for exercise.
Q5John's score on different tests are 104, 84, 88, 84, 100, 90 and 92. Find the mode of the scores.

A. 104
B. 91.71
C. 84
D. 90

Step: 1
The mode is the score that occurs most frequently.
Step: 2
104, 84, 88, 84, 100, 90 and 92
[Original scores.]
Step: 3
84, 84, 88, 90, 92, 100 and 104
[Arrange in order.]
Step: 4
84 occurred two times and no other score occurred more than one time.
Step: 5
So, the mode is 84.
Q6Find the median of the data set 2, 4, 8, 3, and 5.

A. 4
B. 4.4
C. 3
D. 2

Step: 1
The middle number of an ordered data set is called the median of the data set.
Step: 2
2, 4, 8, 3, and 5
[Original data set.]
Step: 3
2, 3, 4, 5, and 8
[Arrange in ascending order.]
Step: 4
The middle number is 4.
Step: 5
So, the median is 4.
Q7Find the mean for the data shown in the line plot.

A. 5
B. 4
C. Green
D. Cannot be determined

Step: 1
The mean of set of data is the sum of all the data values divided by the number of data values.
Step: 2
The number of 'x' symbols over each name indicate the number of occurrences of the name in the data set.
Step: 3
Mean for the data cannot be calculated as we cannot mathematically add (Brown + Brown + Brown + Blue +Blue +Blue +Blue + Hazel + Hazel + Hazel +Hazel +Hazel + Hazel + Green +Green +Green ).
[Mean cannot be determined for categorical data.]
Step: 4
So, the mean for the data cannot be determined.
Correct Answer is :   Cannot be determined
Q8Find the mode for the data shown in the line plot, which depicts the favorite topics in mathematics for grade 9 students.

A. Probability
B. Algebra
C. Statistics
D. Geometry

Step: 1
From the line plot, number of students who like Geometry, Algebra, Statistics and Probability are 5, 6, 4 and 1 respectively.
Step: 2
The mode is the data value that appears most often in a set of data.
Step: 3
The highest number of occurrences in the line plot is for Algebra.
Step: 4
So, the mode for the data shown in the line plot is Algebra.
Q9The table shows the numbers of TV Anchors in six states. Find the mean number of the TV Anchors.
 State Number of TV Anchors California 15 Los Angles 12 New Jersey 18 New York 15 Texas 18 Wyoming 18

A. 17
B. 18
C. 16
D. 15

Step: 1
The total number of TV Anchors for the states = 15 + 12 + 18 + 15 + 18 + 18 = 96
Step: 2
Number of States (data values) = 6
Step: 3
Mean = Sum of the number of TV Anchors the number of states = 966 = 16
Step: 4
The mean number of TV Anchors in the states is 16.
Q10The age (in years) of the children playing in a park are 7, 10, 6, 7, 12, 10, 7, 12, 7, and 6. Find the median age of the children.

A. 10
B. 12
C. 6
D. 7

Step: 1
Median is the middle data value of a set of ordered data.
Step: 2
The ordered data set is 6, 6, 7, 7, 7, 7, 10, 10, 12, and 12.
Step: 3
As there are 10 data values in the set, the median of the data set is the average of the middle two numbers.
Step: 4
So, the median of the data set = 7 + 72 = 7.
Step: 5
So, the median age of the children is 7.
Q11Find the mode of the set of letters.
A, B, D, N, F, X, B, A, G, B

A. C
B. C, B
C. Q
D. B

Step: 1
Mode of a data set is the data value that appears most often.
Step: 2
As B occurs 3 times, the mode of the set of data is B.
[B appears for maximum number of times.]
Q12Find the median for the data set, which shows the scores of 10 students in Jim's class.
67, 62, 66, 63, 68, 69, 69, 69, 64, and 79

A. 69
B. 67.5
C. 68
D. 67

Step: 1
Median is the middle data value of the ordered data set.
Step: 2
The ordered data set is 62, 63, 64, 66, 67, 68, 69, 69, 69, and 79.
Step: 3
As there are 10 data values in the set of data, the median of the data set is the average of the middle two numbers.
Step: 4
So, the median of the data set = 67 + 682 = 1352 = 67.5.
Q13What is the median for the data set 5, 3, 8, 9, 17,12, 13, 33, 25, 31, and 21?
A. 12
B. 25
C. 17
D. 13

Step: 1
The middle number of an ordered data set is called the median of the data set.
Step: 2
5, 3, 8, 9, 17,12, 13, 33, 25, 31, and 21
[Original data set.]
Step: 3
3, 5, 8, 9, 12, 13, 17, 21, 25, 31, and 33
[Arrange the data set in ascending order.]
Step: 4
The median of the data set, the middle number, is 13.
Q14Determine the mode of the data set.
46, 43, 29, 35, 20, 25, 14, 57, 46, 4, 57, 29, 46, and 5

A. 53
B. 32
C. 32.57
D. 46

Step: 1
The number that occurs most frequently in a data set is called the mode.
Step: 2
46, 43, 29, 35, 20, 25, 14, 57, 46, 4, 57, 29, 46, and 5
[Original scores.]
Step: 3
4, 5, 14, 20, 25, 29, 29, 35, 43, 46, 46, 46, 57, and 57
[Arrange in ascending order.]
Step: 4
Since the number 46 appears the greatest number of times, the mode of the data set is 46.
Q15Jessica sells apples. She put apples in 10 baskets and sold them at different prices. The line plot shows the prices of different baskets containing apples. Find the mode.

A. 12
B. 22
C. 2
D. 30

Step: 1
Mode is a number that occurs most often in a data set.
Step: 2
In the line plot shown, there are more crossmarks (x's) above the number 12.
Step: 3
So the mode is $12. [It means that the most number of apple baskets that Jessica has cost$12 each.]