Create a frequency distribution histogram. The table below gives data for the fructose concentration in 100 samples of fruit juice. Plot a histogram showing the frequency distribution of the data. Write a brief description of the important features of the distribution. $$ \begin{aligned} &\text { Fructose content }\left(g L^{-1}\right) \text { in fruit juice }\\\ &\begin{array}{|r|r|r|r|r|r|r|r|r|r|} \hline 11.1 & 14.2 & 13.5 & 9.8 & 12.0 & 13.9 & 14.1 & 14.6 & 11.0 & 12.3 \\ \hline 13.4 & 12.9 & 12.9 & 10.0 & 13.1 & 11.8 & 12.6 & 10.7 & 8.1 & 11.2 \\ \hline 13.8 & 12.4 & 12.9 & 11.3 & 12.7 & 12.4 & 14.6 & 15.1 & 11.2 & 9.7 \\ \hline 11.3 & 14.7 & 10.8 & 13.3 & 11.9 & 11.4 & 12.5 & 13.0 & 11.6 & 13.1 \\ \hline 9.3 & 13.5 & 14.6 & 11.2 & 11.7 & 10.9 & 12.4 & 12.0 & 12.1 & 12.6 \\ \hline 10.9 & 12.1 & 13.4 & 9.5 & 12.5 & 11.6 & 12.2 & 8.8 & 10.7 & 11.1 \\ \hline 10.2 & 11.7 & 10.4 & 14.0 & 14.9 & 11.5 & 12.0 & 13.2 & 12.1 & 13.3 \\ \hline 12.4 & 9.4 & 13.2 & 12.5 & 10.8 & 11.7 & 12.7 & 14.1 & 10.4 & 10.5 \\ \hline 13.3 & 10.6 & 10.5 & 13.7 & 11.8 & 14.1 & 10.3 & 13.6 & 10.4 & 13.9 \\ \hline 11.7 & 12.8 & 10.4 & 11.9 & 11.4 & 10.6 & 12.7 & 11.4 & 12.9 & 12.1 \\ \hline \end{array} \end{aligned} $$

Step by step solution

01

Organize the data into frequency bins

To create frequency bins, the range of the data needs to be divided into a series of intervals, called bins. The bins should be of equal size. In this case, the smallest value is 8.1 and the largest is 15.1. One might choose a bin size of 1, yielding bins of 8-9, 9-10, 10-11, and so on up to 14-15.

02

Count frequency for each bin

After creating the bins, count how many data points fall into each bin. For example, how many samples have a concentration between 8.0 and 8.9, 9.0 and 9.9, and so on.

03

Plot the histogram

The x-axis represents the fructose concentration from 8 to 15 (divided into bins) and the y-axis represents the count of samples. Each bin (interval of concentration) formed into a vertical bar reaching up to the count of samples for that range.

04

Describe the distribution

Examine the shape of the histogram. Communication about the center, spread, and skewness should all be part of this description. Note if the data appears to be normally distributed, skewed to one side or the other, or if there are any outliers apparent.

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