Histograms Please view this tutorial and answer the follow-up questions on loose leaf to turn in to...

Histograms

Please view this tutorial and answer the follow-up questions on loose leaf to

turn in to your teacher.

Histogram Basics

• A statistical graph that measures the frequency of a set of data

• The x-axis can be set up as intervals of one or more depending on the values of the data

• The y-axis always represents frequency (how often a value or range of values occurs)

Example

Station

July High Temperature

(oF)Anchorage, AK 65Mobile, AL 91Los Angeles, CA 84Atlanta, GA 88Des Moines, IA 87Boston, MA 82Helena, MT 85Buffalo, NY 80Philadelphia, PA 86Houston, TX 93Milwaukee, WI 80

What will be the title on your x-axis?

The x-axis should be labeled “Temperature (oF)” because each value in the list is a high temperature.

Example

Station

July High Temperature

(oF)Anchorage, AK 65Mobile, AL 91Los Angeles, CA 84Atlanta, GA 88Des Moines, IA 87Boston, MA 82Helena, MT 85Buffalo, NY 80Philadelphia, PA 86Houston, TX 93Milwaukee, WI 80

Why shouldn’t the names of the cities included on the x-axis?

Because the x-axis represents the range of temperatures not the specific temperature for each city.

NEVER include categories as labels for the x-axis of a

histogram!

Set up your title and labels

Temperatures (oF)

July High Temperatures (oF)

The temperatures range from 65 to 93. What should be the minimum and scale for the x-axis?

60 65 70 75 80 85 90 95

0

1

2

3

4

5

The y-axis ALWAYS measures frequency and should ALWAYS start at zero and count by ones.

Adding Data to the Histogram

Temperatures (oF)


60 65 70 75 80 85 90 95

0

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2

3

4

5The bar between 65 and 70 goes up to 1 on the y-axis because there is only one value (65) in this range.

How high will the bar be between 80 and 85?

Values on a tick mark are counted in the bar to the right!

Adding Data to the Histogram

Temperatures (oF)


60 65 70 75 80 85 90 95

0

1

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4

5

Correct! The bar between 80 and 85 will go up to 4 on the y-axis.

Here is the completed histogram.

Making a Histogram on the Calculator

Let’s look at the July temperatures again, but this time we’ll make the histogram on the calculator.

First, you’ll need to put your information into a list.

Hit STAT

You’ll be taken to this screen.

Edit is highlighted already so just hit ENTER.


Type each number from the data set into your list. You’ll need to hit ENTER after each

number.

Once your information is in the list, you need to set a window. What are the minimum and maximum in the data set?


Our minimum is 65 and our maximum is 93.

We can use the same minimum and maximum that we used when we made the histogram by hand.

xmin = 60 and xmax = 95

Remember, when setting a window you need to go a little

smaller than your minimum and a little higher than your

maximum.


Xmin = 60Xmax = 95

What should we count by here?

We also need to figure out what to count by (xscl). Again, try to pick “nice numbers” that end in zeros or fives and that

are easy to count by.

Since our range is 35, we should count by 5.


Xmin = 60Xmax = 95

Xscl = 5

Hit WINDOW.

Next, we’ll need to put these values into our window.

Now enter your information.

Your ymin can always be -3 and your ymax should be around 10

for a histogram.


Hit 2nd then Y=.

Now that our WINDOW is set, we need to turn the histogram on.

Since Plot 1 is already selected, just hit ENTER.


Select “On” then hit ENTER.

Select the histogram icon by hitting the right arrow

then ENTER.Tell the calculator

where your information is.

(Ex. L1)

Now hit GRAPH.


You should see this histogram!

Now hit GRAPH.

Now, let’s look at the shapes of different histograms.

Shapes of Histograms

Skewed to the right – tail is on the right

Skewed to the left – tail is on the left

Bimodal – two peaksSymmetric – mirror image on both sides

Analyzing the Histogram


Temperatures (oF)60 65 70 75 80 85 90 95

0

1

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4

5 Which shape best represents our histogram?



Temperatures (oF)60 65 70 75 80 85 90 95

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5

Skewed to the left!Notice that the tail is on the left.



Temperatures (oF)60 65 70 75 80 85 90 95

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5 What is the minimum and maximum value in our data set?

65 is the minimum and 95 is the maximum.



Temperatures (oF)60 65 70 75 80 85 90 95

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5

If you said 80-90 is the max, you want to think about the largest value on the x-axis that has a bar touching it.

For the minimum, you want to find the smallest value that is touching a bar (not the smallest value on the x-axis).



Temperatures (oF)60 65 70 75 80 85 90 95

0

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5

Is there a peak in this data set? If so, where?

The peak for this data set is between 80 and 90 with a frequency of 4. It is the highest point in the graph.



Temperatures (oF)60 65 70 75 80 85 90 95

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5

Are there gaps in the histogram? If so, where are they?

There is one gap from 70 to 80 in this data set.

60 to 65 is not a gap because there is no bar before 60.

Gaps MUST have a beginning and an end.



Temperatures (oF)60 65 70 75 80 85 90 95

0

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Are there any outliers in this data set? If so, where and why? If not, why not?

There are no outliers (unusually high or low values) because the bar at 65 to 70 is only two spaces away.

A bar must be at least 3 spaces away from the rest of the data to be considered an outlier.

Now It’s Your Turn!

• Use what you’ve just reviewed to help you answer the following questions.

• Submit any graphs on graph paper along with answers to each question to your teacher. (These do not need to be included on the wikispace!)

High School Graduation Rates for the 50 United States by Percentage

58 55 76 63 8765 75 70 62 6358 80 85 62 5875 70 57 89 7865 85 71 71 9072 76 83 73 7674 68 83 67 7266 58 65 76 7653 72 75 71 8058 74 83 54 78

Make a histogram of the data. Remember to include all important information. Once you’ve completed the histogram, move on to the next slide to answer some questions.

Follow-Up Questions

1. Describe the shape of the histogram. 2. What are the minimum and maximum?3. What is the peak of the histogram?4. Are there any gaps in the histogram? If so,

where. If not, why not.5. Are there any outliers in the histogram. If so,

where. If not, why not.

Follow-Up Questions6. Describe the distribution of this histogram using as many descriptors as possible.

Histograms Please view this tutorial and answer the follow-up questions on loose leaf to turn in to...

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