The following data values represent the number of homeruns a baseball player hit

Question

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.)

Explanation / Answer

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

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