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Then/Now You have already found the mean or average of a data set. (Lesson 2–5) Use the mean, median, and mode as measures of central tendency. Choose an appropriate measure of central tendency and recognize measures of statistics.

Vocabulary measures of central tendency mean median mode For a list of numerical data, numbers that can represent the whole set of data (ex. Mean, median, mode) The sum of the data divided by the number of items in the data set, also called average In a set of data, the middle number of the ordered data, or the mean of the two middle numbers The number that occur(s) most often in a set of data

Example 1 Find Measures of Central Tendency MOVIES Find the mean, median, and mode of the data in the table. The mean is million.

Example 1 Find Measures of Central Tendency To find the median, order the numbers from least to greatest. 373, 377, 380, 404, 423, 431, 435, 436, 461, 601 There is an even number of items. Find the mean of the two middle numbers The median is 427 million. There are no repeated values, so there is no mode. Answer: mean: $432.1 million, median: $427 million, no mode

A.A B.B C.C D.D Example 1 CYP A.mean, 73.9; median, 85; no mode B.mean, 83.3; median, 85; mode, 85 C.mean, 750; median, 62; mode, 85 D.mean, 83.3; median, 62; mode, 85 TEST SCORES The test scores for a class of nine students are 85, 93, 78, 99, 62, 83, 90, 75, 85. Find the mean, median, and mode of the test scores.

Example 2 Nabuko has test scores of 80, 85, 72, and 91. If her next score is 82, which of the following statements would be true? Read the Test Item You need to determine which statement would be true if Nabuko’s score on her next test is 82. AThe mean increases and the median decreases. BThe mean is unchanged and the median decreases. CBoth mean and median increase. DBoth mean and median decrease.

Example 2 Solve the Test Item Adding another score of 82 will not change the mean. You can eliminate choices A, C, and D. Arrange the numbers from least to greatest, first with four days and then with five days. Find the median to check that choice B is correct. 72, 80, 85, 91 The median is , 80, 82, 85, 91 The median is 82. The mean of the four scores is

Example 2 Answer: The correct answer is B. So, the median would decrease.

A.A B.B C.C D.D Example 2 CYP A.The mean increases and the median decreases. B.The mean is unchanged and the median decreases. C.The mean and the median increase. D.The mean and the median decrease. Sheila has test scores of 85, 82, 70 and 90. If her next score is 78, which of the following statements would be true?

Concept B

Example 3 Choose an Appropriate Measure SURVEYS Mai took a poll in her class to see how many times her classmates visited the local amusement park during summer vacation: 4, 0, 2, 3, 2, 4, 1, 2, 1, 2, 3, 2, 2, 0. What measure of central tendency best represents the data? Then find the measure of central tendency. Answer: The set of data has many repeated values, so the mode would be the best. The most frequent value is 2.

A.A B.B C.C D.D Example 3 CYP A.mean B.median C.mode D.cannot be determined BOWLING Jenny’s bowling scores are 108, 138, 140, 142, 139, 138, and 145. Which measure of central tendency best represents the data?

Example 4 Different Points of View SALARIES The weekly salaries for the employees at Bob’s Book Store are $600, $600, $625, $1250, $1800. Which measure of data should Bob’s Book Store’s manager use to show new employees that the salaries are high? Median: 600, 600, 625, 1250, 1800 Mean: 625 Mode: 600

Example 4 Different Points of View Answer: The manager would want to use the highest measure for salary. So, the manager would want to use the mean, $975. The greatest measure is the mean.

A.A B.B C.C D.D Example 4 CYP A.mode B.median C.mean D.cannot be determined EXERCISE The number of hours spent exercising each week by a group of women are: 1, 6, 4, 2, 1, and 8. Which measure of central tendency should a person use to show that women do not spend enough time exercising?

End of the Lesson