Section 2-3 Histograms

Key Concept

We use a visual tool called a histogram to analyze the shape of the distribution of the data.

Histogram

A graph consisting of bars of equal width drawn adjacent to each other (without gaps). The horizontal scale represents the classes of quantitative data values and the vertical scale represents the frequencies. The heights of the bars correspond to the frequency values.

HistogramBasically a graphic version of a frequency distribution.

HistogramThe bars on the horizontal scale are labeled with one of the following:

(1) Class boundaries

(2) Class midpoints

(3) Lower class limits (introduces a small error)

Horizontal Scale for Histogram: Use class boundaries or class midpoints.

Vertical Scale for Histogram: Use the class frequencies.

Relative Frequency Histogram Has the same shape and horizontal scale as a histogram, but the vertical scale is marked with relative frequencies instead of actual frequencies.

Objective is not simply to construct a histogram, but rather to understand something about the data.

When graphed, a normal distribution has a “bell” shape. Characteristic of the bell shape are

Critical ThinkingInterpreting Histograms

(1) The frequencies increase to a maximum, and then decrease, and

(2) symmetry, with the left half of the graph roughly a mirror image of the right half.

The histogram on the next slide illustrates this.

Critical ThinkingInterpreting Histograms

Critical ThinkingInterpreting Histograms

Example 1: What is the class width? What are the approximate lower and upper class limits of the first class?

Bell shape:

Example 2: The histogram below represents the number of television sets per household for a sample of U.S. households. How many households are included in the histogram?

Example 3: The histogram below represents the number of television sets per household for a sample of U.S. households. How many households have 4 televisions?

Example 4: The histogram below represents the number of television sets per household for a sample of U.S. households. What is the maximum number of households that have the same number of television sets?

Example 5: In a survey, 20 people were asked how many magazines they had purchased during the previous year. The results are shown below. Construct a histogram to represent the data. Use 4 classes, with a class width of 10,and begin with a lower class limit of –0.5. Does the distribution appear to be normal?

6 15 3 36 25 18 12 18 5 3024 7 0 22 33 24 19 4 12 9

Press the STAT button.Choose “1. Edit”

Enter your data in L1 Press “2nd Y=”(STAT PLOT)

Choose “1: Plot 1…”Make your screen look like this:

(turn it ON and choose histogram)Press “Zoom”

Choose “9:ZoomStat”Press “Trace” and use the arrow buttons to move the cursor around your Histogram to determine class widths and frequencies.

Histograms on the Calculator