A distribution of numbers has the following fivenumber summa

A distribution of numbers has the following five-number summary: 10.0, 15.0. 30.9. 50.0. 63.7 True or False? These numbers can be used to calculate the standard deviation of the distribution. True False

Solution

True

10.0, 15.0, 30.9, 50.0, 63.7

Mean = (10.0 + 15.0 + 30.9 + 50.0 + 63.7)/5 = 848/25

==> mean = 33.92

Now standard deviation = {[(10.0 - 33.92)² + (15.0 - 33.92)²+ (30.9 - 33.92)² + (50.0 - 33.92)² + (63.7 - 33.92)²]/5}

==> (2084.668/5)

==> 416.9336

==> 20.419

Hence standard deviation = 20.419