Using the Mean to Find Data

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Presentation transcript:

Using the Mean to Find Data Lesson 7 Data Analysis Using the Mean to Find Data

Warm-Up Find the mean, median and mode of the following data sets: 42, 46, 46, 50, 58, 58, 64 16, 24, 29, 17, 19, 18, 21, 28 What is the mean of: , , , ? Write your answer as a fraction.

Using the Mean to Find Data Targets: Use the formula for mean to find missing numbers in data sets. Find the range of data sets.

Example 1 Jasmine needs to average 62 seconds or less in four preliminary heats to make the final cut for the girls 400-meter team. Jasmine ran the first three heats in 60.4, 59.9 and 62.1 seconds. What is the slowest time she can get in the fourth heat and still make the cut? She will run 4 heats. Multiply by 4. Subtract previous times. 248 – 60.4 – 59.9 – 62.1 = 65.6 Jasmine needs to run the final heat in 65.6 seconds or less to make the final cut.

Vocabulary Range: The difference between the maximum (largest value) and minimum (smallest value) values in a data set.

Range = Maximum – Minimum Maximum is the largest number in the data set. Minimum is the smallest number in the data set.

Example 2 What is the range of the following data sets? 17, 29, 33, 34, 38, 40 Maximum: 40 Minimum: 17 Range = 40 – 17 = 23 26, 37, 40, 33, 35, 38 Minimum: 26 Range = 40 – 26 = 14

Example 3 The following ordered data set has a range of 33 and a mean of 37. What are the two missing data pieces? 21, 26, 31, 31, 38, ___, 43, 49, ___ Range = Maximum – Minimum 33 = x – 21 + 21 + 21 54 = x

Example 3 (continued) The following ordered data set has a range of 33 and a mean of 37. What are the two missing data pieces? 21, 26, 31, 31, 38, ___, 43, 49, 54 There are 9 values. Mean = 37. Multiply by 9. Subtract other terms. 333 – 21 – 26 – 31 – 31 – 38 – 43 – 49 – 54 = 40 The missing values are 40 and 54.

Exit Problems Find the missing number in the following data sets. 39, 28, 33, 36, 25, ___ Mean = 32 7, −2, −4, 3, ___ Mean = 6.2 What is the range of the following data set? 82, 77, 85, 92, 89, 99, 79, 85 Find the missing numbers in the following ordered data set. ___, 20, 20, 22, 22, ___, 34 Mean = 23 Range = 20

Communication Prompt Write a story problem where the mean could be used to find a missing number in a data set. Solve your problem.