Question

1. A university asked 10 graduate students how many hours of homework they were planning to do that week. Here are their responses:

14 13 15 21 19 24 25 28 25 31

A. What's the mean number of hours of homework done by the students per week? What is the median? Why are these figures different?

B. What is the range of data?

C. Is the data skewed? If so, in what direction? How do you know?

Please show all calculations. Also please show all calculations in typing rather than writing. Thank you kindly.

Answer 1

A. Firstly we need to arrange the raw data in increasing order. The ordered data is as follows:

13 14 15 19 21 24 25 25 28 31

Now mean = (total of all observations)/ (total no. Of observations) = 215/10 = 21.5

Median = middle most value of the given observations

= any value between 21 and 24

But for uniqueness we take the average of these two values which is = 22.5

The 3rd part of question A. Will be answered later please follow the answer.

B. Range of the data = 31 - 13 = 18

C. To know about skewness of the given data we need to find mode of the data which is 25 (most frequently obtained. 2 times)

Now we can see that for the given data

Mean < median < mode

So the data is negatively skewed.

Now I am coming to the question A. 3 rd part

As the data is negatively skewed , the value of mean is different from value of median. If the variable is symmetrically distributed then there will be a chance for median and mean to be equal.