The following table gives the scores of 30 students in

Pretoto4o

Pretoto4o

Answered question

2021-11-27

The following table gives the scores of 30 students in a mathematics examination:
Scores90998089707960695059Students481242
Find the mean and the standard deviation of the distribution of the given data.

Answer & Explanation

Maked1954

Maked1954

Beginner2021-11-28Added 17 answers

Step 1
The formula for mean and standard deviation is given by,
E(X)={x×f(x)}n
sample variance, V(X)=(xmean)2f(x)n1
SD=V(X)
Step 2
The mean and standard deviation are calculated using the following table.
ScoreStudents(f)Midpoint(x)fxf((xmean)2)9099494.53781201.7777788089884.5676430.222222270791274.589485.333333336069464.5258641.77777785059254.51091027.555556Total3023153386.666667
Step 3
The mean and standard deviation is calculated as follows:
Mean=231530
=77.1667
Sample variance =3386.66666729
=116.7816
standard deviation =116.7416
=10.8066

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