Questions: Given the following frequency distribution table for a set of data about the heights of vertical jumps (in inches) for all an exercise class, construct a histogram that accurately summarizes the data. Vertical Jump Height (in inches) Frequency 14.5-15.5 3 15.5-16.5 5 16.5-17.5 11 17.5-18.5 9 18.5-19.5 8 19.5-20.5 4

Given the following frequency distribution table for a set of data about the heights of vertical jumps (in inches) for all an exercise class, construct a histogram that accurately summarizes the data.

Vertical Jump Height (in inches) Frequency
14.5-15.5 3
15.5-16.5 5
16.5-17.5 11
17.5-18.5 9
18.5-19.5 8
19.5-20.5 4

Transcript text: Given the following frequency distribution table for a set of data about the heights of vertical jumps (in inches) for all an exercise class, construct a histogram that accurately summarizes the data. \begin{tabular}{|c|c|} \hline \begin{tabular}{c} Vertical Jump Height \\ (in inches) \end{tabular} & Frequency \\ \hline $14.5-15.5$ & 3 \\ \hline $15.5-16.5$ & 5 \\ \hline $16.5-17.5$ & 11 \\ \hline $17.5-18.5$ & 9 \\ \hline $18.5-19.5$ & 8 \\ \hline $19.5-20.5$ & 4 \\ \hline \end{tabular}

Solution

Solution Steps

To construct a histogram from the given frequency distribution table, we need to plot the vertical jump height intervals on the x-axis and their corresponding frequencies on the y-axis. Each bar in the histogram will represent a height interval, and the height of the bar will correspond to the frequency of that interval.

To solve the given problem, we will follow the steps to construct a histogram based on the provided frequency distribution table.

Step 1: Understand the Data

The data provided is a frequency distribution table for vertical jump heights in inches. The table is as follows:

| Vertical Jump Height (in inches) | Frequency | |----------------------------------|-----------| | 14.5-15.5 | 3 | | 15.5-16.5 | 5 | | 16.5-17.5 | 11 | | 17.5-18.5 | 9 | | 18.5-19.5 | 8 | | 19.5-20.5 | 4 |

Step 2: Determine the Histogram Structure

A histogram is a graphical representation of the distribution of numerical data. It is an estimate of the probability distribution of a continuous variable. The x-axis will represent the vertical jump height intervals, and the y-axis will represent the frequency of each interval.

Step 3: Plot the Histogram

To plot the histogram, follow these steps:

Draw the x-axis and label it with the intervals: 14.5-15.5, 15.5-16.5, 16.5-17.5, 17.5-18.5, 18.5-19.5, and 19.5-20.5.
Draw the y-axis and label it with the frequency values, ranging from 0 to the maximum frequency, which is 11 in this case.
For each interval, draw a bar that reaches up to the corresponding frequency value.