Solved Examples and Worksheet for Measures of Central Tendency
A. 83
B. 86
C. 85
D. 84
Step: 1
Average test score = S u m o f a l l t h e t e s t s c o r e s N u m b e r o f s u b j e c t s
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 = 510 6
[Simplify.]
Correct Answer is : 85
A. 23 lb
B. 20 lb
C. 22 lb
D. 21 lb
Step: 1
Mean weight = S u m o f t h e w e i g h t s N u m b e r o f l i s t e d w e i g h t s
Step: 2
Sum of the weights = 9 + 31 + 14 + 11 + 49 + 34 + 15 + 5
Step: 3
= 168 lb
[Add the weights.]
Step: 4
Number of listed weights = 8
Step: 5
Mean weight = 168 8
[Substitute and simplify.]
Step: 6
So, the mean weight of the data set is 21 lb.
Correct Answer is : 21 lb
A. 25
B. 17
C. 24
D. 22
Step: 1
Average score = total score number of games
[Formula for average.]
Step: 2
= 2 4 + 1 6 + 2 4 + 2 6 + 2 0 5
[Substitute the values.]
Step: 3
= 110 5
[Add the values in the numerator.]
Step: 4
= 22
[Divide.]
Step: 5
So, Ethan's average score was 22.
Correct Answer is : 22
| 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+41 7
[Substitute the values given in the table.]
Step: 3
= 161 7
[Add the values in the numerator.]
Step: 4
= 23
[Divide.]
Step: 5
So, Lauren spent a mean time of 23 minutes daily for exercise.
Correct Answer is : 23
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.
Correct Answer is : 84
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.
Correct Answer is : 4
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
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.
Correct Answer is : Algebra
| 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 96 6
Step: 4
The mean number of TV Anchors in the states is 16.
Correct Answer is : 16
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 + 7 2
Step: 5
So, the median age of the children is 7.
Correct Answer is : 7
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 = 6 7 + 6 8 2 135 2
Correct Answer is : 67.5
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.
Correct Answer is : 13
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.
Correct Answer is : 46
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.]
Correct Answer is : 12
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