Question

Calculate the mean, variance and standard deviation for the following distribution:Class       30-40    40-50      50-60      60-70      70-80      80-90       90-100Frequency   3             7             12          15             8            3               2

Answer 1

With the given distribution , `x_i = 35, 45, 55, 65, 75, 85, 95`
`f_i = 3, 7,12, 15,8,3,2`
`:. x_i f_i = 105, 315,660,975,600,255,190`
`:. sum f_i = 50`
`sum x_i f_i = 3100`
`:. Mean(barX) = (sum x_i f_i)/(sum f_i) = 3100/50 = 62`
Now, `|x_i - barx| = 27, 17,7,3,13,23, 33`
`|x_i - barx|^2 = 729, 289,49,9, 169,529, 1089`
`:. |x_i - barx|^2f_i = 2187,2023,588,135,1352,1587, 2178`
`:.` Variance, `(sigma)^2 = (sum |x_i - barx|^2f_i)/ (sum f_i) = 10050/50 = 201 `
Standard deviation, `(sigma) = sqrt201 ~= 14.177.`