Calculating the Mean and Median of a Data Set: Background You’ll Need 2

Illustrating Frequency with Histograms

Below we are given a histogram for the variable Hours of Sleep Per Night (Weekend). Recall that a histogram displays the distribution of a quantitative variable but, unlike the dotplot in which each observation is stacked above each value appearing, a histogram gathers groups of observations up into its bars.

recall

You may wish to refresh your understanding of how data is represented in a histogram.

Core skill:

Use the following histogram to address Questions 4-7.

A histogram of labeled "Hours of Sleep Per Night (Weekend)" on the x-axis and "Count" on the y-axis. For 4-5, the count is approximately 4. For 5-6, the count is approximately 8. For 6-7, the count is approximately 33. For 7-8, the count is approximately 57. For 8-9, the count is approximately 70. For 9-10, the count is approximately 54. For 10-11, the count is approximately 23. For 11-12, the count is approximately 4. For 12-13, the count is approximately 2.

As you did with for the dotplot above, first orient yourself to the information conveyed in the histogram by answering Question 4.  Then, compare and contrast the histogram to the dotplot in Question 5. Finally, read and interpret the histogram to answer Questions 6 and 7.

question 4

Now that you are familiar with the information presented in the histogram, look back at the dotplot and consider general differences and similarities in the two types of displays.

question 5

Histograms are more commonly encountered than dotplots as a visualization of quantitative data since they can more concisely display large data sets. Dotplots are more appropriate for smaller sets of data in which the observations (the dots) are not overwhelmingly numerous.

Now use the histogram to answer questions about the variable Hours of Sleep Per Night (Weekend).

question 6

question 7

Let’s examine the distribution of a variable from another data set.

The histogram below displays the frequency of sodium content per serving for [latex]20[/latex] different varieties of cereals.[1]

A histogram labeled "Cereal Sodium Content (mg)" on the horizontal axis, which is numbered in increments of 50 from 0 to 100, and labeled "Count" on the vertical axis. For 0-25, the count is 1. For 50-75, the count is 2. For 100-125, the count is 1. For 125-150, the count is 3. For 150-175, the count is 2. For 175-200, the count is 4. For 200-225, the count is 5. For 275-300, the count is 1. For 325-350, the count is 1.

question 8

question 9

  1. Agresti, A., Franklin, C. A., & Klingenberg, B. (2021). Statistics: The art and science of learning from data, 5th edition. Pearson. https://www.pearson.com/us/higher-education/program/Agresti-My-Lab-Statistics-with-Pearson-e-Text-Access-Card-for-Statistics-The-Art-and-Science-of-Learning-from-Data-18-Weeks-5th-Edition/PGM2788191.html ↵