Murder Rate The data represent the murder rate per 10000 ind

Murder Rate: The data represent the murder rate per 100,00 individuals in a sample of selected cities in the United States. Find the variance and standard deviation. Class limits 5-11 12-18 19-25 26-32 33-39-40-46 Frequency 8 5 7 1 1 3. Please included the steps and I\'m just a little confused. Thank you

Solution

First prepare a frequency distribution table as follows:

For finding std deviation we find mid point of each class interval and take it as x.
Frequency is marked as f

Mean = sum of all xf/sum of all f = 487/25

=19.48

E(X^2) = sum of x^2f/25

=508.36

Hence var(x) =508.36-19.48^2

= 128.8896

Std dev = 11.3593