Every year, colleges and universities collect data on their entering class. Below are the writing scores for entering college freshmen:

64.5, 43.7, 56.7, 56.7, 46.3, 64.5, 39.1, 39.1, 51.5, 64.5, 43.7, 41.1, 59.3, 51.5, 65.1, 59.3, 56.7, 54.1, 43, 56.7, 54.1, 47.6, 35, 48.9, 54.1, 64.5, 33.3, 38.5, 67.1, 59.3, 61.9

Calculate the following statistics for the given data:

a) Mean =
b) Min =
c) Max =
d) Range =
e) Variance =
f) Standard Deviation =

To analyze the writing scores of entering college freshman, we calculate the mean, min, max, range, variance, and standard deviation of the data set.

Explanation:

a) mean = the average of a set of numbers. To find the mean, add up all the numbers in the set and divide by the total number of values. In this case, the mean is calculated by adding up the writing scores and dividing by the total number of scores, which is 30.

b) min = the smallest value in a set of numbers. To find the min, simply look for the smallest value in the set. In this case, the min is 33.3.

c) max = the largest value in a set of numbers. To find the max, simply look for the largest value in the set. In this case, the max is 67.1.

d) range = the difference between the max and min values. To find the range, subtract the min from the max. In this case, the range is 67.1 - 33.3 = 33.8.

e) variance = a measure of how spread out the values in a set are. To find the variance, subtract the mean from each value in the set, square the differences, find the average of the squared differences, and take the square root. In this case, the variance is (sum of squared differences)/(total number of values).

f) standard deviation = the square root of the variance. To find the standard deviation, take the square root of the variance. In this case, the standard deviation is the square root of the variance calculated in part e).

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