Lesson 8 Data Analysis Completing Data Sets

Warm-Up Glen sold 20, 29 and 22 popsicles in three days. To sell an average of 25 popsicles per day for four days, how many must Glen sell on day 4? Kirby wants to run an average of 1.5 miles per day each week. The first six days of this week he ran a total of 8 miles. How many miles does Kirby need to run on the seventh day to meet his goal? What are the missing numbers in the ordered data set? 52, ___, 64, 66, 66, 68, ___ Range = 19 and Mean = 64

Completing Data Sets Target: Use statistics and problem-solving to find missing numbers in data sets.

Example 1 Karina weighed ten different frogs and put the weights in order. She found her measures of center before her paper got splattered with mud. Find the missing weights. ___, 7.1, 7.2, 7.4, 7.5, ___, 8.7, 9.1, 9.1, 11.5 Mean = 8.23, Median = 7.7 The median is 7.7, but there are two middle numbers:

Example 1 (continued) ___, 7.1, 7.2, 7.4, 7.5, 7.9, 8.7, 9.1, 9.1, 11.5 Mean is 8.23 and there are 10 values. Sum of values = 8.23(10) = 82.3. Subtract all known values: 82.3 – 7.1 – 7.2 – 7.4 – 7.5 – 7.9 – 8.7 – 9.1 – 9.1 – 11.5 = 6.8 The two missing values are 6.8 and 7.9.

Example 2 Tony was given the following statistics about his seven test scores in Geography class: Range = 19, Mode = 83 and 84, Median = 84, Mean = 86. He remembers his highest test score was a 97. What were his other test scores? Tony has seven tests: __, __, __, __, __, __, __ Highest score was 97: __, __, __, __, __ , __, 97 Range was 19: 97 – 19 = 78 78, __, __, __, __, __, 97 Median is 84: 78, __, __, 84, __, __, 97 Modes are 83 and 84: 78, 83, 83, 84, 84, __, 97

Example 2 (continued) Tony was given the following statistics about his seven test scores in Geography class: Range = 19, Mode = 83 and 84, Median = 84, Mean = 86. He remembers his highest test score was a 97. What were his other test scores? 78, 83, 83, 84, 84, __, 97 Mean of 7 tests is 86. Sum of values = 86(7) = 602. Subtract other values: 602 – 78 – 83 – 83 – 84 – 84 – 97 = 93 His test scores are: 78, 83, 83, 84, 84, 93, 97

Exit Problems Find the missing number in the following data sets. 17, 24, 19, 12, 27, ___ Median = 21 28, 35, 45, 29, 40, 38, ___ Median = 35, Range = 27 Find the missing numbers in the ordered data set. ___, 19, ___, 29, ___, 33 Range = 18, Median = 27, Mean = 25

Communication Prompt Rate your understanding of these “Completing Data Sets” problems on a scale of 1-5. (1 means you are having a very difficult time, 5 means that you find them to be very easy). Describe why you gave yourself that rating. What are you having the most difficulty with? What can the teacher do to help you?