Question

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. 
   
3. What is the median of this data set?
   
4. What is the mode of this data set?
5. 
   
6. Here is the second data set.
   

   30

   22

   41

   38

   47

   39

   79

   36

   38

   70

7. 
   
8. What is the mean (¯xx¯) of this data set?
9. 
   
10. What is the median of this data set?
11. 
    
12. What is the mode of this data set?

Answer 1

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