Solve for the mean, variance and standard deviation. A university

shelbs624c

shelbs624c

Answered question

2021-12-04

Solve for the mean, variance and standard deviation.
A university asked its applicants to write a short essay for its entrance test. Based on their gathered data, it was found out that two out 10 students did not make grammatical mistakes, three out of 10 students made a grammatical mistake, four out of 10 students made two mistakes, and one out of 10 made three grammatical mistakes. What is the average number of grammatical mistakes made by the students in the essay?

Answer & Explanation

Liek1993

Liek1993

Beginner2021-12-05Added 13 answers

Step 1
Let X be the random variable representing the number of grammatical mistakes in the short essay.
The following Probability Distribution Table gives the probability of the discrete random variable X,
X0123P(X)210310410110
The average (or mean) no. of grammatical mistakes, is calculated as,
μ=xP(X)
=(0×210)+(1×310)+(2×410)+(3×110)
=0+310+810+310
=1410
=1.4
Thus, the mean or average number of grammatical errors is 1.4
Step 2
Solve for the Standard Deviation as,
σ=1N(xμ)2
14[(01.4)2+(11.4)2+(21.4)2+(31.4)2]
=14[1.96+0.16+0.36+2.56]
=5.04
=2.245
Thus, the standard deviation of the number of grammatical errors is approximately 2.245
Solve for the Variance as,
Var(X)=(Standard Deviation)2
=(2.245)2
=5.04
Thus, the variance of the number of grammatical errors is 5.04

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