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EXAMPLE 2 Finding Median, Mode, and Range Find the median, mode(s), and range of the numbers below. 64 60 64 38 52 65 61 48 SOLUTION Write the numbers in order from least to greatest. 38 48 52 60 61 64 64 65 Median:Because there is an even number of data values, the median is the mean of the two middle values. Median = 60 + 61 2 = 121 2 = 60.5

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EXAMPLE 2 Range: Find the difference between the greatest and the least values. Range = 65 – 38 = 27 Mode: The number that occurs most often is 64. Finding Median, Mode, and Range

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EXAMPLE 3 Choosing the Best Average Dance-a-Thon: You receive the pledge amounts listed below for your participation in a dance-a-thon. Which average best represents the pledge amounts? $1 $8 $12 $10 $45 $9 $1 $7 $6 The mean suggests that most pledges are greater than they actually are. = $11 1 + 8 + 12 + 10 + 45 + 9 +1 + 7 + 6 9 Find the mean: STEP 1 SOLUTION

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EXAMPLE 3 STEP 2 Find the median: 1 1 6 7 8 9 10 12 45 The median is $ 8. It is the middle value of the nine values. STEP 3 Find the mode: The pledge that occurs most often is $ 1. The mode suggests that most pledges are less than they actually are. The median best represents the pledge amounts. ANSWER Choosing the Best Average

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EXAMPLE 3 STEP 4 Find the range: $45 – $1 = $44 The range suggests that the data are more evenly spaced than they are. The median best represents the pledge amounts. ANSWER Choosing the Best Average

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EXAMPLE 4 Standardized Test Practice SOLUTION Mean = 300 + 120 20 420 = 20 = 21 To find the mean cost of the trees, divide the sum of the costs by the total number of trees purchased. ANSWER The mean cost of the trees is $21. The correct answer is B.

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GUIDED PRACTICE for Examples 2, 3, and 4 Find the median, mode(s), and range. 3. 9, 13, 19, 14, 16, 11, 7, 6, 13 ANSWER 13; 13; 13 4. 18, 52, 23, 79, 66, 17, 20, 10 ANSWER 21.5; no mode ; 69

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GUIDED PRACTICE In Example 3, you receive three more pledges of $15, $20, and $22. Which measure best represents the pledge amounts? ANSWERmedian for Examples 2, 3, and 4 What If? 5.

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GUIDED PRACTICE 6. What are the mode and median costs of the trees in Example 4 ? ANSWER 20; 20 for Examples 2, 3, and 4

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The number which appears most often in a set of numbers. Example: in {6, 3, 9, 6, 6, 5, 9, 3} the Mode is 6 (it occurs most often). Mode : The middle number.

The number which appears most often in a set of numbers. Example: in {6, 3, 9, 6, 6, 5, 9, 3} the Mode is 6 (it occurs most often). Mode : The middle number.

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