Question

 The test scores of 40 students are summarized in the frequency distribution below. Find the standard deviation. Score Students 50-59 5 60-69 8 70-79 6 80-89 13 90-99 8

Answer 1

Mean $\bar{X} = \frac{\sum f_iX_i}{N} = \frac{3090}{40}=77.25$

Standard deviation $= \sqrt{\frac{\sum f_iX_i^2}{N} - (\bar{X})^2}$

$= \sqrt{ \frac{245700}{40} -(77.25)^2} \\ = \sqrt{6142.5 -5967.56} \\ = \sqrt{174.94} \\ = 13.22$