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Wize University Statistics Textbook > Displaying & Summarizing Quantitative Data

Histograms

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Histograms

A histogram is a useful graph that show the frequency (or counts) of quantitative data, sorted in class intervals or bins.


Watch Out!
Do not confuse a histogram with a bar chart, which is used to showcase categorical data.

PAGE BREAK
A histogram is is a very common graph used to let us see the spread, center, and shape of a distribution of one quantitative variable.

Spread
  • What’s the range (i.e. max – min)?
  • Does the data cover a large or small range of values?
  • This is important when comparing two or more histograms.

Center
  • Locate the middle. Where is it?
  • The mean and median are both are measures of center. The location of the mean and median depends on the shape.

Shape
  • Is the distribution symmetric, skewed, or has no clear shape?

Other observations
  • Any gaps? Gaps are empty bins where the frequency is zero.
  • Outliers? Outliers are extreme values that a far from the rest of the distribution at either side of the histogram.
  • Peaks/modes?
  • Unimodal, bimodal, or multimodal?

There are four sections in STAT 100, each with 54 students. The distributions of grades for each section are shown below in histograms.


Which distribution has the highest median grade?
There are four sections in COMM 499, each with 54 students. The distributions of grades for each section are shown below in histograms.


Which distribution shows the greatest variability in grades?

Practice: Histogram

Below is a histogram showing how many glasses of water a person drinks per week (n=168). Which of the following is true? [Select all that apply]


Extra Practice
Histograms
The quiz scores for 3 different stats classes are displayed in the following histograms. Which class has the smallest standard deviation and the largest mean, respectively?
Histograms
The following 3 histograms summarize the heights of children in 3 different day care groups, each with 50 children.
Fill in the following statments with A, B or C
Mode of
C
> Mode of
A
>Mode of
B
Histograms
The following histogram shows the distribution of the number of STAT 151 classes attended by 20 students in the Winter 2019 semester. In each class interval, the left enpoint is included but not the right.
What percent of these students attended 20 or more classes but fewer than 30 classes?
Histograms
The quiz scores for 3 different stats classes are displayed in the following histograms. Which class has the smallest standard deviation and the largest mean, respectively?
Histograms
Practice: Comparing Histograms
The following 3 histograms summarize the heights of children in 3 different day care groups, each with 50 children.
Fill in the following statments with A, B or C
Histograms
Which of the following could be the median of the histogram above?
Histograms
Melanie keeps track how many emails she can respond to during a shift. The frequency refers to the number of emails:
Melanie was able to respond to 91 emails today. What will happen?
Histograms
Melanie keeps track how many emails she can respond to during a shift. The frequency refers to the number of emails:
Which of ones are TRUE and which are FALSE:
a) The distribution is roughly symmetric.
Histograms
Which of the following could be the IQR of the histogram above?
Histogram
Problem
Which of the following could be the median of the histogram above?
Histograms
Melanie was able to respond to 91 emails today. If we add this additional data to the histogram, what will happen?
Histograms
The histogram refers to the number of emails Melanie responds to during a day at work:
Which of the following is true?
Histograms and Time Series
Vinnie sells cashmere scarves all year round. His sales are shown in a time series:
Which histogram matches the time series plot above?
Histograms
We randomly sample 168 people and ask them how many glasses of wine they drink per week.
Here is the histogram:
What can you say about the shape of this histogram?
Histograms
There are four sections in STAT 123, each with 80 students. The distributions of grades for each section are shown below in histograms.
Which of the following is true? (Check all that applies.)
Histograms, Skewness and Symmetry
The histogram refers to the number of emails Melanie responds to during a day at work:
Which of the following is true?
Histograms, Skewness and Symmetry
Melanie was able to respond to 91 emails today. If we add this additional data to the histogram, what will happen?