A study by researchers at the University of Maryland...

A study by researchers at the University of Maryland addressed the question of whether the mean body temperature of humans is $98.6^{\circ} \mathrm{F}$. The results of the study by P. Mackowiak et al. appeared in the article "A Critical Appraisal of $98.6^{\circ} \mathrm{F},$ the Upper limit of the Normal Body Temperature, and Other Legacies of Carl Reinhold August Wunderlich" (Journal of the American Medical Association, Vol. 268, pp. 1578-1580). Among other data, the researchers obtained the body temperatures of 93 healthy humans, as provided on the WeissStats CD. Use the technology of your choice to obtain and interpret a. a frequency histogram or a relative-frequency histogram of the temperatures. b. a dotplot of the temperatures. c. a stem-and-leaf diagram of the temperatures. d. Compare your graphs from parts (a)-(c). Which do you find most useful?

A study by researchers at the University of Maryland addressed the question of whether the mean body temperature of humans is $98.6^{\circ} \mathrm{F}$. The results of the study by P. Mackowiak et al. appeared in the article "A Critical Appraisal of $98.6^{\circ} \mathrm{F},$ the Upper limit of the Normal Body Temperature, and Other Legacies of Carl Reinhold August Wunderlich" (Journal of the American Medical Association, Vol. 268, pp. 1578-1580). Among other data, the researchers obtained the body temperatures of 93 healthy humans, as provided on the WeissStats CD. Use the technology of your choice to obtain and interpret
a. a frequency histogram or a relative-frequency histogram of the temperatures.
b. a dotplot of the temperatures.
c. a stem-and-leaf diagram of the temperatures.
d. Compare your graphs from parts (a)-(c). Which do you find most useful?

Key Concepts

Data Visualization Comparison

Comparing different data visualizations, such as histograms, dotplots, and stem-and-leaf diagrams, enables one to select the most appropriate method based on the dataset and specific analytical objectives. Each visualization offers unique insights—while histograms are ideal for large datasets and showing overall trends, dotplots and stem-and-leaf diagrams preserve individual data points critical for detailed analysis.

Stem-and-Leaf Diagram

A stem-and-leaf diagram divides each data point into a 'stem' and a 'leaf', preserving the original data while showing its distribution. The diagram helps in identifying the shape, spread, and central tendency of data, and it is particularly useful for spotting modes and gaps in the dataset.

Frequency Histogram

A frequency histogram is a graphical representation of data where the data is grouped into bins or intervals and the frequency of data values within each bin is indicated by the height of a bar. This type of visualization is useful for understanding the overall distribution of data, identifying peaks, gaps, and spotting potential outliers.

Relative-Frequency Histogram

A relative-frequency histogram is similar to a frequency histogram, but it expresses the height of each bar as a proportion or percentage of the total number of data points instead of raw counts. This normalization allows for easier comparison across data sets of different sizes and a more intuitive understanding of the data distribution.

Dotplot

A dotplot is a simple statistical tool that depicts each individual data point as a dot along a number line. Each dot represents a single observation, which makes dotplots especially useful for small or moderate-sized data sets where the focus is on the exact data values and their frequency.

Transcript

00:01 So a frequency is to grab is going to have the frequency on the y -axis and the numbers on the x -axis, the numbers being kind of like the bins of the range of what is happening.

00:11 And in this case, it's a body temperature.

00:14 So maybe we'll have the 94 degrees fahrenheit and then the 95 degrees.

00:20 And then we'll have like a lot more than the 96 is with the 96 to 97.

00:27 We're going to see a huge bump there.

00:28 Then we'll probably see something like this.

00:31 So this is going to be a relative frequency histogram where this is the frequency, and these are the temperatures, where this bin is most likely going to be 96 .8, and you're probably going to be going by however the data fits up.

00:50 You want to make sure that you have a nice even shape and something that doesn't look super boxy and super big like this.

00:59 As this tells you more than this does.

01:03 And you'll be finding out a couple of, after grouping your data appropriately, you'll see that some graphs look a little bit more like this, some histograms, and then some other histograms are going to look a little bit more blocky like that.

01:17 And this one right here is going to be the preferred one to choose from.

01:23 A dot plot is also going to be the same thing.

01:26 It's going to find a lot, you're going to find a lot, of dot plots, all the dots and the dot plot are going to be a lot in here...

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