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

2. 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)

3. Example Station July High Temperature ( o F) Anchorage, AK65 Mobile, AL91 Los Angeles, CA84 Atlanta, GA88 Des Moines, IA87 Boston, MA82 Helena, MT85 Buffalo, NY80 Philadelphia, PA86 Houston, TX93 Milwaukee, WI80 What will be the title on your x-axis? The x-axis should be labeled “Temperature ( o F)” because each value in the list is a high temperature.

4. Example Station July High Temperature ( o F) Anchorage, AK65 Mobile, AL91 Los Angeles, CA84 Atlanta, GA88 Des Moines, IA87 Boston, MA82 Helena, MT85 Buffalo, NY80 Philadelphia, PA86 Houston, TX93 Milwaukee, WI80 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!

5. Set up your title and labels Frequency Temperatures ( o F) July High Temperatures ( o F) The temperatures range from 65 to 93. What should be the minimum and scale for the x- axis? 6065707580859095 0 1 2 3 4 5 The y-axis ALWAYS measures frequency and should ALWAYS start at zero and count by ones.

6. Adding Data to the Histogram Frequency Temperatures ( o F) July High Temperatures ( o F) 6065707580859095 0 1 2 3 4 5 The 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!

7. Adding Data to the Histogram Frequency Temperatures ( o F) July High Temperatures ( o F) 6065707580859095 0 1 2 3 4 5 Correct! The bar between 80 and 85 will go up to 4 on the y-axis. Here is the completed histogram.

8. 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.

9. Making a Histogram on the Calculator 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?

10. Making a Histogram on the Calculator 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.

11. Making a Histogram on the Calculator Xmin = 60 Xmax = 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.

12. Making a Histogram on the Calculator Xmin = 60 Xmax = 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.

13. Making a Histogram on the Calculator Hit 2 nd then Y=. Now that our WINDOW is set, we need to turn the histogram on. Since Plot 1 is already selected, just hit ENTER.

14. Making a Histogram on the Calculator 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.

15. Making a Histogram on the Calculator You should see this histogram! Now hit GRAPH. Now, let’s look at the shapes of different histograms.

16. Shapes of Histograms Skewed to the right – tail is on the right Skewed to the left – tail is on the left Bimodal – two peaks Symmetric – mirror image on both sides

17. Analyzing the Histogram July High Temperatures ( o F) Frequency Temperatures ( o F) 6065707580859095 0 1 2 3 4 5 Which shape best represents our histogram?

18. Analyzing the Histogram July High Temperatures ( o F) Frequency Temperatures ( o F) 6065707580859095 0 1 2 3 4 5 Skewed to the left! Notice that the tail is on the left.

19. Analyzing the Histogram July High Temperatures ( o F) Frequency Temperatures ( o F) 6065707580859095 0 1 2 3 4 5 What is the minimum and maximum value in our data set? 65 is the minimum and 95 is the maximum.

20. Analyzing the Histogram July High Temperatures ( o F) Frequency Temperatures ( o F) 6065707580859095 0 1 2 3 4 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).

21. Analyzing the Histogram July High Temperatures ( o F) Frequency Temperatures ( o F) 6065707580859095 0 1 2 3 4 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.

22. Analyzing the Histogram July High Temperatures ( o F) Frequency Temperatures ( o F) 6065707580859095 0 1 2 3 4 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.

23. Analyzing the Histogram July High Temperatures ( o F) Frequency Temperatures ( o F) 6065707580859095 0 1 2 3 4 5 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.

24. 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!)

25. High School Graduation Rates for the 50 United States by Percentage 5855766387 6575706263 5880856258 7570578978 658571 90 7276837376 7468836772 66586576 5372757180 5874835478 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.

26. 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.

27. Follow-Up Questions 6. Describe the distribution of this histogram using as many descriptors as possible.