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.)

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