89.7k views
2 votes
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.)

1 Answer

1 vote
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
User Dakeyras
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories