The following data represent the annual rainfall distribution in St. Louis, Missouri, for a sample of 25 years from 1870 to 2004. Rainfall (inches) Number of Years 20 − 24 1 25 − 29 3 30 − 34 5 35 − 39 8 40 − 44 5 45 − 49 2 50 − 54 0 55 − 59 1 Check the empirical relation of mean, median and mode for the above data.
Answers
Given : data of the annual rainfall distribution in St. Louis, Missouri, for a sample of 25 years from 1870 to 2004
To find : mean, median and mode
Solution:
Rainfall (inches) F CF Mean A =(mean-37)/5 f* A
20 - 24 1 1 22 -3 -3
25 - 29 3 4 27 -2 -6
30 - 34 5 9 32 -1 -5
35 - 39 8 17 37 0 0
40 - 44 5 22 42 1 5
45 - 49 2 24 47 2 4
50 - 54 0 0 52 3 0
55 - 59 1 25 57 4 4
25 -1
Mean = 37 + 5 * (-1)/25
= 37 - 0.2
= 36.8
20 - 24 = 19.5 - 24.5 & so on
35 - 39 = 34.5 - 39.5
Median = 34.5 + 5* (25/2 - 9)/8
= 34.5 + 2.19
= 36.69
Mode = 34.5 + 5* ( 8 - 5)/(8 - 5 + 8 - 5)
= 34.5 + 2.5
= 37
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