Question

Question 1:

Which of the following description best explains why the median may be a better measure to describe the number of hours slept than the mode or mean?

Question 2:

Which measure of central tendency (the mean, median or the mode) best describes the pattern of data for Saturday night? What about for Tuesday night? Explain and defend your answer. Make sure you take a look at the data before you answer this question, and think about whether there are outliers (extreme scores) in either the Tuesday or Saturday datasets.

Data:

Below are some data from 35 college students about the total number of hours they slept on Saturday night (the data are made up, but they do actually reflect real patterns of what sleep looks like in college students!). You'll need these data to answer the next several questions.

Number of Hours Slept on Saturday Night

10, 9, 8, 8, 8, 10, 10, 12, 12, 9, 8, 8, 12, 8, 12, 10, 9, 9, 14, 6, 8, 7, 8, 10, 8, 12, 9, 8, 12, 6, 8, 9, 8, 10, 7

- Mean for Tuesday = 5.71

- Mode for Tuesday = 8.00

- Median for Tuesday = 6

Below are some data from 35 college students about the total number of hours they slept on Tuesday night (the data are made up, but they do actually reflect real patterns of what sleep looks like in college students!). You'll need these data to answer the next several questions.

Number of hours slept on Tuesday Night:

6, 5, 8, 5, 3, 0, 8, 4, 8, 5, 8, 6, 4, 6, 8, 8, 6, 6, 2, 4, 4, 7, 6, 5, 4, 6, 5, 6, 5, 4, 8, 8, 5, 8, 9

- Mean for Saturday = 9.2

- Mode for Saturday = 8.00

- Median for Saturday = 9

Answer 1

1) The number of hours slept on Tuesday night best explains the situation so as to why the median is a better measure to describe the number of hours slept by the student than mean or mode.

This is because the data of the number of hours slept on Saturday night contains outliers such as hour count -- 0. In these situations, the mean, as well as the mode, is affected by the outliers in a deceptive manner. Median is considered as the best measure of central tendency in this case.

2) As per Saturday night's records, we find that the mean and the median do not differ much, the range is lesser than that of Tuesday's night so we do not consider any outlier here and moreover, one-third of the data points contain "8" as the sleeping hour's record. Thus here the mode = 8 becomes the best measure to describe the pattern of the data.

Since for the Tuesday night's records, the range of sleeping hours is more, and also there is the presence of outliers, we consider Median = 6 as the best measure to describe the pattern of the data, which is not affected by the skew present in the data.