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**Histograms & Comparing Graphs**

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**Focus 6 Learning Goal – (HS. S-ID. A. 1, HS. S-ID. A. 2, HS. S-ID. A**

Focus 6 Learning Goal – (HS.S-ID.A.1, HS.S-ID.A.2, HS.S-ID.A.3, HS.S-ID.B.5) = Students will summarize, represent and interpret data on a single count or measurement variable. 4 3 2 1 In addition to level 3.0 and above and beyond what was taught in class, the student may: · Make connection with other concepts in math · Make connection with other content areas. The student will summarize, represent, and interpret data on a single count or measurement variable. - Comparing data includes analyzing center of data (mean/median), interquartile range, shape distribution of a graph, standard deviation and the effect of outliers on the data set. - Read, interpret and write summaries of two-way frequency tables which includes calculating joint, marginal and relative frequencies. The student will be able to: - Make dot plots, histograms, box plots and two-way frequency tables. - Calculate standard deviation. - Identify normal distribution of data (bell curve) and convey what it means. With help from the teacher, the student has partial success with summarizing and interpreting data displayed in a dot plot, histogram, box plot or frequency table. Even with help, the student has no success understanding statistical data.

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What are Histograms? A histogram is a graphical display of data using bars of different heights. Each bar represents the frequency of an event occurring in an equal sized interval. Histograms are used to analyze large sets of quantitative data. Frequency of

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Shapes of Histograms What do you notice about the possible shapes of histograms compared to the possible shapes of dot plots?

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**How to make a histogram:**

Daily high temperatures in degrees Fahrenheit: Determine the range of your data. Lowest number 44. Highest number 71. Range = 27 Determine appropriate equal intervals. 5 numbers per interval. Make a frequency table with the intervals. Put a tally mark in the appropriate interval for each number. Verify that you have the same number of tally marks as you have items of data.

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**How to make a histogram:**

Create a graph. Label the x- axis with the intervals from the frequency table. Label the y- axis “Frequency.” Draw each bar to the appropriate height. The bars must touch each other, no gaps between bars unless there are no data points for that interval. F R E Q U N C Y

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Comparing Graphs The dot plot shows the ages of people who are grandparents living in the Aprende neighborhood. How does a dot plot compare to a histogram? When is it better to use a dot plot?

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Comparing Graphs Box plots can be created side by side to compare two sets of data on the same scale. This box plot shows average monthly rainfall for Miami, FL and New Orleans, LA. Which city shows a greater range in average monthly rainfall? Explain how the parallel box plots makes it easy to compare the ranges in this case. How do the maximums, minimums, and the medians of the two data sets compare?

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Comparing Graphs The test scores of students in a math class are as follows: 80, 72, 82, 80, 80, 80, 88, 88, 84, 92, 92, 96, 70, 90, 98, 92, 88, 92, 90, 80, 84 Which graph is best for finding out the most common test score? Which graph is best if you want to know how many people scored a B on the test? Which graph is best for a teacher who wants to know the range of scores for the bottom 25%, the middle 50% and the top 25%?

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