professor smith took a sample of 186 students from her morning class and a sampl

Question

professor smith took a sample of 186 students from her morning class and a sample of 128 students from her evening class. On exam 1, all those sampled from the morning class got an average 73 and those sampled in the evening got an average of a 67 with a variance of 123. If Professor smith combines these two samples, what is the combined Exam 1 average? What is the combined Exam 1 median? What is the shape of the combined Exam 1 grade distribution? What is the combined exam 1 standard deviation?

Explanation / Answer

There are two samples as morning and evening.

Morning class has parameters :

n1 = 186

X1bar = 73

Evening class parameters :

n2 = 128

X2bar = 67

If Professor smith combines these two samples, what is the combined Exam 1 average?

XbarC = n1X1bar + n2X2bar / n1+n2

= (186*73 + 128*67) / 186+128 = 70.55

What is the shape of the combined Exam 1 grade distribution?

The shape of the exam1 distribution is normal since both the samples are of too large.

What is the combined exam 1 standard deviation?

First we find variance then we find standard deviation.

Variance = (n1s1^2 + n2s2^2 + n1(X1bar - XbarC)2  + n2(X2 bar- XbarC)2 ) / n1+n2

= (186*123 + 128*123 + 186(73-70.55)2 + 128*(67-70.55)2 ) / (186+128)

Variance = 131.69

Standard deviation = sqrt(131.69) = 11.48

What is the combined Exam 1 median?

For normal distribution mean = median

Therefore median = 70.55

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