Question

in the claims department of an insurance office various quantities are computed at the end of each days business. On monday 10 claims are received for a particular class of policy. the mean claim amount is calculated to be K4,260 and the standard deviation to be K1120. On Tuesday it found that one of mondays claims for K5450 was classified wrongly and it is removed from the set of 10 claims. calculate the resulting mean and standard deviation of the reduced set of 9 claims.

Answer 1

total claim amount on Monday:

$4260\cdot10=42600$

total claim amount on Tuesday after removing one claim:

$42600-5450=37150$

so, resulting mean:

$37150/9=4127.78$

standard deviation:

$\sigma=\sqrt{\frac{\sum (x_i-\mu)^2}{n}}$

on Monday:

$\sigma=\sqrt{\frac{\sum (x_i-4260)^2}{10}}=1120$

then:

$\sum x_i^2-2\cdot 4260\sum x_1+10\cdot 4260^2=10\cdot 1120^2$

$\sum x_i^2=306916000$

on Tuesday:

$\sum x_i^2-5450^2-2\cdot 4127.78(\sum x_1-5450)+9\cdot 4127.78^2=9\cdot \sigma_1^2$

$\sigma_1=3709.85$