A sample of college students reported they owned the following number of books a

Question

A sample of college students reported they owned the following number of books

a. What is the mean number of books owned?

b. What is the median number of books owned?

c. What is the mean absolute deviation of the number of books owned?

d. What is the standard deviation of the number of books owned?

e. What is the advantage of the coefficient of variation? please calculate the CV.

f. What is the first quartile?

g. What is the thrid quartile?

h. what is the interquartile range?

i. what is the coefficient of skewness developed by pearson

j. what is the shape of distribution

k. According to Chebyshev's theorem, at least what percent of the number of books owned will lie between 62 and 78?

l. Does the data set have any outliers?

m. Make a box-whiskers plot

Explanation / Answer

a. The mean of a data set is the sum of the terms divided by the total number of terms. Using math notation we have:

Mean=Sum of terms/Number of terms

In this example:

Sum of terms /Number of terms=560/8=70

b. the median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

52   64   66   69   74   76   79   80   

As you can see, we do not have just one middle number but we have a pair of middle numbers, so the median is the average of these two numbers:

Median=69+74/2=71.5

c. MAD = median(|xi - median(xi)|)=6.5

d.

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