Problem

The grades for 20 students on the most recent exam are given in the data table below. Round your answers to 2 decimal places as needed
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Mean =

Median =

Standard deviation =

Minimum score =

Highest score =

Answer

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Answer

So, the mean is 68.35, the median is 65, the standard deviation is 17.06, the minimum score is 41, and the highest score is 92

Steps

Step 1 :First, list all the scores in ascending order: 41, 41, 42, 46, 49, 52, 54, 57, 58, 72, 73, 75, 76, 79, 82, 83, 85, 88, 92, 92

Step 2 :Calculate the mean by summing all the scores and dividing by the number of scores: 41+41+42+46+49+52+54+57+58+72+73+75+76+79+82+83+85+88+92+9220=68.35

Step 3 :Find the median by taking the average of the 10th and 11th scores: 58+722=65

Step 4 :Calculate the squared differences from the mean: (4168.35)2,(4168.35)2,(4268.35)2,...,(9268.35)2

Step 5 :Calculate the average of these squared differences to get the variance: (4168.35)2+(4168.35)2+(4268.35)2+...+(9268.35)220=291.1775

Step 6 :Take the square root of the variance to get the standard deviation: 291.1775=17.06

Step 7 :The minimum score is the lowest score: 41

Step 8 :The highest score is the highest score: 92

Step 9 :So, the mean is 68.35, the median is 65, the standard deviation is 17.06, the minimum score is 41, and the highest score is 92

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