Question

In: Statistics and Probability

We are going to calculate the mean, median, and mode for two sets of data. Please...

We are going to calculate the mean, median, and mode for two sets of data. Please show your answer to one decimal place if necessary.

Here is the first data set.

22 76 25 85 28 29 72 22 95 50 23


  1. what is the mean (¯xx¯) of this data set?

  2. What is the median of this data set?
  3. What is the mode of this data set?

  4. Here is the second data set.
    30 22 41 38 47 39 79 36 38 70

  5. What is the mean (¯xx¯) of this data set?

  6. What is the median of this data set?

  7. What is the mode of this data set?

Solutions

Expert Solution

Solution:

The formulas for the mean, median, and mode are given as below:

Mean = Sum of all observations / total number of observations

Median = Middle most observation (in case of odd sample size) when numbers are in an increasing (or decreasing) order

Median = average of middle most two observations (in case of even sample size) when numbers are in an increasing (or decreasing) order

Mode = The observation with highest frequency

The calculation table for the first data set is given as below:

No.

X

1

22

2

22

3

23

4

25

5

28

6

29

7

50

8

72

9

76

10

85

11

95

Total

527

Mean

47.90909

Median

29

Mode

22

Sample size = n = 11 (odd number)

Mean = 527/11 = 47.90909

Median = 29

Mode = 22

The calculation table for second data set is given as below:

No.

X

1

22

2

30

3

36

4

38

5

38

6

39

7

41

8

47

9

70

10

79

Total

440

Mean

44

Median

38.5

Mode

38

Sample size = 10 (Even number)

Mean = 440/10 = 44

Median = (38 + 39)/2 = 38.5

Mode = 38


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