In Exercises 9–18, construct the histograms and answer the giv...

Question

In Exercises 9–18, construct the histograms and answer the given questions.

Analysis of Last Digits Use the frequency distribution from Exercise 21 in Section 2-1 to construct a histogram. What can be concluded from the distribution of the digits? Specifically, do the heights appear to be reported or actually measured?

Accepted Answer

Hi, everyone, let's take a look at this practice problem. This problem says to create a histogram using the frequency distribution of the last digits of reported package weights in kilograms as shown below. What conclusion can be drawn from the digit distribution? Do the weights appear to have been reported or actually measured? And below the text we have a table that contains two columns, one labeled last digit and the other labeled frequency. Under the last digit column, we have the values of 012345678, and 9, and under the frequency column, we have the values of 856759675, and 21. So the first thing we need to do is construct a histogram using either a spreadsheet software or manually draw it on graph paper. But in either case, on the X-axis, we're going to plot the last digit, and on the Y axis, we're going to plot the corresponding frequencies. And we're actually going to draw a vertical bar with the heights equal to the frequencies for each last digit. Doing so, we will get the following histogram. Where we have plotted the digits 0 through 9 on the X axis, and we have our frequency on the Y axis. And so, for each of our digits, we've drawn a vertical bar to the height matching the frequency for that digit. So for 0, we have a frequency of 8, for 1, we have a frequency of 5, or 2, we have a frequency of 6, or 3, we have a frequency of 7. For 4, we have a frequency of 5. For 5, we have a frequency of 9. For 6, we have a frequency of 6, for 7, we have a frequency of 7. For 8, we have a frequency of 5, and for 9, we have a frequency of 21. So this here is the histogram that the problem was looking for. Next, we need to determine if the values appear reported or actually measured. And so we're going to be looking at two different patterns. First, we're going to be looking for uniformity, and if the digits were randomly measured, then they should appear roughly uniform in frequency, meaning they all have approximately the same frequency. And this other pattern we'll look at is for a digit preference. So, if certain digits appear significantly more often, that would indicate human bias in reporting values. And if you look at our histogram, we see that the last digit 9 appears much more frequently than the others. Which contrasts a natural randomly measured data set, which should have a more uniform distribution of last digits. And so, we can conclude that the pattern suggests that the data may have been reported rather than actually measured, as people tend to round numbers to preferred digits like 9 or 5. So that means that the answer to the second half of our question is actually reported. So I hope that this explanation has been useful, and I'll see you in the next video.

Key Concepts

Histogram

Frequency Distribution

Reported vs. Measured Data

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