Question

The following table gives the scores of 30 students in a mathematics examination. Scores 90–99 80–89 70–79 60–69 50–59 Students 3 7 12 4 4 Find the mean and the standard deviation of the given data. Hint: Assume that all scores lying within a group interval take the middle value of that group. (Round your answers to two decimal places.)

Answer 1

The given data is
Scores:      90-99  80-89  70-79  60-69  50-59
Students:   3          7           12        4          4
Because we are to take the middle value for each group.
Therefore the total score is
Sx = 3*94.5 + 7*84.5 + 12*74.5 + 4*64.5 + 4*54.5 = 2245
The number of students is 3+7+12+4+4 = 30

The mean is
m =2245/30 = 74.833

Calculate (Sx - m)² 
(Sx - m)² = 3*(94.5-74.833)² + 7*(84.5-74.833)² + 12*(64.5-74.833)²
               + 4*(64.5-74.833)² + 4*(54.5-74.833)² =  3896.7

Calculate the standard deviation
s = √(3896.7/29) = 11.592

Answer:
mean = 74.83
std. deviation = 11.59