Listed below are the numbers of home runs in major league baseball for each year beginning...
Listed below are the numbers of home runs in major league baseball for each year beginning with 1990.
3317 3383 3038 4030 3306 4081 4962 4640 5064 5528
Find the median
Find the variance
Homework Answers
Solution:
| x | x2 |
| 3317 | 11002489 |
| 3383 | 11444689 |
| 3038 | 9229444 |
| 4030 | 16240900 |
| 3306 | 10929636 |
| 4081 | 16654561 |
| 4962 | 24621444 |
| 4640 | 21529600 |
| 5064 | 25644096 |
| 5528 | 30558784 |
| ∑x=41349 | ∑x2=177855643 |
a ) Median :
Observations in the ascending order are :
3038,3306,3317,3383,4030,4081,4640,4962,5064,5528
Here, n=10 is even.
M=Value of(n/2)thobservation+Value of(n2+1)thobservation2
=Value of(10/2)thobservation+Value of(10/2+1)thobservation2
=Value of5thobservation+Value of6thobservation2
=4030+40812
=4055.5
b ) Sample Variance S2=∑x2-(∑x)2nn-1
=177855643-(41349)210/9
=177855643-170973980.1/9
=6881662.9/9
=764629.2111
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