The following data values represent the number of homeruns a

The following data values represent the number of homeruns a baseball player hit each year during his 25-year baseball career. Complete parts a. through d. below. 16 37 25 47 27 45 42 26 22 32 44 12 49 28 38 24 15 37 12 35 17 30 24 22 33 a. Calculate the mean of these data values. Round to two decimal places as needed.) Calculate the standard deviation of these data values S-D(Round to two decimal places as needed) b. Group this data into four classes with class boundaries of 10-under 20, 20-under 30, 30-under 40, and 40-under 50 Group Frequency c. Calculate the approximate mean of these grouped data values. Round to two decimal places as needed) 10-under 20 20-under 30 30-under 40 40-under 50 h\" (Round to one decimal place as needed.)

Solution

Answers a, b and c are given in the tabular format below:

We can clearly see that there is some difference and that can be attributed to the fact that the  Part a uses the actual data points whereas part c assumes the mid-points to be a good representation of the data points.

This however, may not be always true. Hence, option B is correct for the last part.

Data
16		Mean	29.56
37		Sample STDEV	10.9965146
25		Population STDEV	10.77433989
47
27
45		Group	Frequency	Mid-point	Product	Mid-pt sqrd	Sum of squares
42		10-Under 20	5	15	75	225	1125
26		20-Under 30	8	25	200	625	5000
22		30-Under 40	7	35	245	1225	8575
32		40-Under 50	5	45	225	2025	10125
44
12		Total	25		745		24825
49
28		Mean	29.8
38
24		Mean Sum of Squares	993
15		Mean^2	888.04
37		Variance	104.96
12
35		Stdev	10.24499878
17
30
24
22
33