Lesson 13-3 Histograms

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Objectives Interpret data displayed by histograms Display data in histograms

Vocabulary Frequency table – Histogram – Measurement classes –

Measures of Central Tendency Mean – average value of the data set Median – the middle value of the ordered data set Mode – the value of the data set that occurs most often Data set: 2, 3, 4, 4, 5, 6, 7, 8, 10 Mean: 2 + 3 + 4 + 4 + 5 + 6 + 7 + 8 + 10 = 49 49/9 = 5.44 Median: 5 (4 elements below and 4 above in ordered list) Mode: 4 (only value that occurs more than once)

Histograms A graph of the frequency for different groups Usually groups have the same width The graph can show the distribution of the data Symmetric, skewed right, skewed left Symmetric (Uniform) Symmetric (Bell-shaped) Skewed Right (tail in right) Skewed Left (tail in left)

Example 1a Student Population In what measurement class does the median occur? Use the histogram below to determine your answer. First, add up the frequencies to determine the number of students in homeroom classes at Central High School. There are 24 homeroom classes, so the middle data value is between the 12th and 13th data values. Both the 12th and 13th data values are located in the 20-25 measurement class. Answer: The median occurs in the 20-25 measurement class.

Example 1b Student Population Describe the distribution of the data in the histogram shown below. Answer: Only two homeroom classes have fewer than 10 students. There is a gap in the 5-10 measurement class. Most of the homeroom classes have at least 15 students. The distribution is skewed to the right.

Example 2 Multiple-Choice Test Item Use the data in the histograms to determine which class has a greater median test score. A Class A B The medians are about the same. C Class B D Cannot be determined

Example 2 cont Group A Group B Study the histograms carefully. The measurement classes and the frequency scales are the same for each histogram. The distribution for Class A is skewed to the right, and the distribution for Group B is skewed to the right. This would indicate that the median heights are about the same. To check this assumption, locate the measurement class of each median. Group A Group B The median is between the 12th and 13th data values. The median is in the 80-90 measurement class. The median is between the 12th and 13th data values. The median is in the 80-90 measurement class. Answer: The median heights are about the same. The answer is B.

Example 3 Football Create a histogram to represent the following scores of top 25 winning college football teams during one week of the 2001 season. 43, 52, 38, 36, 42, 46, 26, 38, 38, 31, 38, 37, 38, 48, 45, 27, 47, 35, 35, 26, 47, 24, 41, 21, 32 Step 1 Identify the greatest and least values in the data set. The scores range from 21 to 52 points. Step 2 Create measurement classes of equal width. For these data, use measurement classes from 20 to 55 with a 5-point interval for each class.

Example 3 cont Step 3 Create a frequency table using the measurement classes. 1 | 5 |||| 3 ||| 9 |||| |||| 2 || Frequency Tally Score Intervals

Example 3 cont Step 4 Draw the histogram. Answer: Use the measurement classes to determine the scale for the horizontal axis and the frequency values to determine the scale for the vertical axis. For each measurement class, draw a rectangle as wide as the measurement class and as tall as the frequency for the class. Label the axes and include a descriptive title for the histogram. Answer:

Summary & Homework Summary: Homework: A Histogram can illustrate information in a frequency table The distribution of data can be determined from a histogram Homework: none