Bonds Devlation Dev Aaron Dev. Ruth Dev.Dev 2 32 1024 4 30 11 23 259 16 19 -31 9

Question

Bonds Devlation Dev Aaron Dev. Ruth Dev.Dev 2 32 1024 4 30 11 23 259 16 19 -31 961 12 13 25 25 26 24 12 35 34 34 37 5.2 39 6.2 5.8 29.2 54.8 108.2 108.2 130.0 130.0 207.4 474.6 5.4 7.4 62 38.A 518 7.2 45 10.4 114 114 144 44 112 125.4 44 112 125.4 44 112 1254 44 112 1254 45 122148.8 47 14.22016 59 25 49 73 0 26 1. Calculate the Standard Deviation of Babe Ruth's home runs first Will Aaron's standard deviation be higher than Ruth's, or lower, or the same? Why? 2. Calculate standard deviations for Aaron: Who is the most "consistent"? How does the Standard Deviation describe this? 3. Highlight or Circle Ruth's seasons where his home runs were within one stendard deviation of the moan. and Bonds: What percentage of his career is that?Show Your Work 4. What percentage of Bonds' home rns are within one standard deviation ofthe mean? Show your work and highlight those seasons. 6. What percentage of Aaron's home nuns are within one standard deviation of the moan? Show your work and highlight those seasons. 8. The 'range rule of thumb" (standard deviation range/4) can be used to ESTIMATE the subetitute for the real method! How wel doos this mathiod work for eh set? Anwer belowr standard devistion; but t is no Ruth Bonds Aaron

Explanation / Answer

Solution

Back-up Theory

Let di be the deviation of the ith observation. Then,

Standard Deviation (SD) = sqrt of [(1/n) [1,n](di2)]

Excel calculations are detailed at the end.

Part (1)

SD of Ruth = 21.0927 ANSWER 1

Since di’s are larger for Ruth as compared to those of Aaron,

SD of Ruth must be higher than SD of Aaron. ANSWER 2

Part (2)

SD of Aaron = 9.8158. ANSWER 3

SD of Bonds = 15.8038. ANSWER 4

Aaron is more consistent than Bonds ANSWER 5

Smaller the SD, more the consistency. ANSWER 6

Part (3)

Run is within 1 SD of the mean => |di| < SD

Visually examining Ruth’s runs, we find that mod of di = - 12, - 9, - 5, 0 and 1 are less than SD. So, 5 out of 10 or 50% are within 1 SD from mean. ANSWER 7

Part (4)

Same as above, for Bonds, all except di = 38.4 are less than the SD. So, 8 out of 9 or 90% are within 1 SD from mean. ANSWER 8

Excel Calculations

i Bonds Aaron Ruth 1 2.4 5.2 -32 2 5.4 6.2 -31 3 7.4 6.2 -30 4 10.4 7.2 -28 5 10.4 7.2 -23 6 11.4 11.2 -12 7 11.4 11.2 -9 8 14.4 11.2 -5 9 38.4 11.2 0 10 12.2 1 11 14.2 sum(di^2) 2247.84 1059.84 4449 sum(di^2)/n 249.76 96.3491 444.9 SD 15.8038 9.81576 21.0927

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