1. CONFIDENTIAL 1 Grade 8 Algebra1 Data Distributions

2. CONFIDENTIAL 2 Warm Up 1) The ages of the applicants for a driver’s license one day are shown in the table. Create a stem-and-leaf plot of the data. 2) The length of a rectangle is one less than two times the width. The area is 15 yd 2. What are the dimensions of the rectangle? 2) length: 5 yd; width: 3 yd

3. CONFIDENTIAL 3 A measure of central tendency describes how data clusters around a value. Data Distributions The mean is the sum of the values in the set divided by the number of values in the set. The median is the middle value when the values are in numerical order, or the mean of the two middle values if there are an even number of values.

4. CONFIDENTIAL 4 The mode is the value or values that occur most often. There may be one mode or more than one mode. If no value occurs more often than another, we say the data set has no mode. The range of a set of data is the difference between the least and greatest values in the set. The range describes the spread of the data.

5. CONFIDENTIAL 5 Finding Mean, Median, Mode, and Range of a Data Set Find the mean, median, mode, and range of each data set. A) The number of hours Isaac did homework on six days: 3, 8, 4, 6, 5, 4. Write the data in numerical order. Add all the values and divide by the number of values. 3, 4, 4, 5, 6, 8 3_+ 4 + 4 + 5 + 6 + 8 6 mean: = 30 = 5 6

6. CONFIDENTIAL 6 4 occurs more often than any other value. median: The median is 4.5. 3, 4, 4, 5, 6, 8 There are an even number of values. Find the mean of the two middle values. mode: = 4 range: = 8 - 3 = 5

7. CONFIDENTIAL 7 B) The weight in pounds of Maria’s five cats: 12, 14, 12, 16, 16. Write the data in numerical order. Add all the values and divide by the number of values. 12, 12, 14, 16, 16 12_+ 12 + 14 + 16 + 16 5 mean: = 70 = 14 5 12 and 16 both occur more often than any other value. median: The median is 14. 12, 12, 14, 16, 16 There are an even number of values. Find the mean of the two middle values. mode: = 12, 16 range: = 16 - 12 = 4

8. CONFIDENTIAL 8 Now you try! Find the mean, median, mode, and range of each data set. 1a. 8, 8, 14, 6 1b. 1, 5, 7, 2, 3 1c. 12, 18, 14, 17, 12, 18 1a. Mean = 9, median = 8, mode = 8, range = 8 1b. Mean = 3.6, median = 3, mode = none, range = 6 1c. Mean = 15 1, median = 15 1, mode = 12,18,range =6 6 2

9. CONFIDENTIAL 9 A value that is very different from the other values in the set is called an outlier. In the data below, one value is much greater than the other values. This causes the mean to be greater than all of the other data values. In this case, either the median or mode would better describe the data.

10. CONFIDENTIAL 10 Choosing a Measure of Central Tendency Niles scored 70, 74, 72, 71, 73 and 96 on six geography tests. Use the mean, median, and mode of his scores to answer each question. mean = 76 median = 72.5 mode: none A) Which value gives Niles’ test average? The average of Niles’ scores is the mean, 76. B) Which value best describes Niles’ scores? Explain. The median score is the best description of Niles’ six scores. Most of his scores were near 72. The mean is higher than most of Niles’ scores because he scored 96 on one test. Since there is no mode, it is not a good description of the data.

11. CONFIDENTIAL 11 2. Josh scored 75, 75, 81, 84, and 85 on five tests. Use the mean, median, and mode of his scores to answer each question. mean = 80 median = 81 mode = 75 a) Which value describes the score Josh received most often? b) Which value best describes Josh’s scores? Explain. 2a. Mode = 75 2b. Median; the mean is lowered by two scores of 75, and the mode is the lowest score. Now you try!

12. CONFIDENTIAL 12 Measures of central tendency describe how data tends toward one value. You may also need to know how data is spread out across several values. Quartiles divide a data set into four equal parts. Each quartile contains one fourth of the values in the set. The inter quartile range (IQR) is the difference between the upper and lower quartiles. The IQR represents the middle half of the data.

13. CONFIDENTIAL 13 A box-and-whisker plot can be used to show how the values in a data set are distributed. The minimum is the least value that is not an outlier. The maximum is the greatest value that is not an outlier. You need five values to make a box-and-whisker plot: the minimum, first quartile, median, third quartile, and maximum.

14. CONFIDENTIAL 14 Sports Application The numbers of runs scored by a softball team in 19 games are given. Use the data to make a box-and-whisker plot. 3, 4, 8, 12, 7, 5, 4, 12, 3, 9, 11, 4, 14, 8, 2, 10, 3, 10, 9 Step 1: Order the data from least to greatest. 2, 3, 3, 3, 4, 4, 4, 5, 7, 8, 8, 9, 9, 10, 10, 11, 12, 12, 14 Step 2: Identify the five needed values and determine whether there are any outliers. IQR: 10 - 4 = 6 1.5 (6) = 9 4 - 9 = -5 10 + 9 = 19 No values are less than -5 or greater than 19, so there are no outliers.

15. CONFIDENTIAL 15 Step 3: Draw a number line and plot a point above each of the five values you just identified. Draw a box through the lower and upper quartiles and a vertical line through the median. Draw lines from the box to the lower and upper extremes. (These are the whiskers.) Half of the scores are between 4 and 10 runs per game. One- fourth of the scores are between 2 and 4. The greatest score earned by this team is 14.

16. CONFIDENTIAL 16 3) Use the data to make a box-and-whisker plot. 13, 14, 18, 13, 12, 17, 15, 12, 13, 19, 11, 14, 14, 18, 22, 23 3) Now you try!

17. CONFIDENTIAL 17 Assessment 1) 85, 83, 85, 82 Find the mean, median, mode, and range of each data set. 2) 12, 22, 33, 34, 44, 44 3) 10, 26, 25, 10, 20, 22, 25, 20 4) 71, 73, 75, 78, 78, 80, 85, 86 1) Mean = 83.75, median = 84, mode = 85, range = 3 2) Mean = 31.5, median = 33.5, mode = 44, range = 32 3) Mean = 19.75, median = 21, mode = 10,20,25, range = 16 4) Mean = 78.25, median = 78, mode = 78, range = 15

18. CONFIDENTIAL 18 5) The distance between five students’ homes and the school are 3, 2, 2, 2, and 15 miles. Use the mean, median, and mode of the distances to answer each question. mean = 2.8 median = 2 mode = 2 a.Which value describes the distance between home and school that occurs most often? b. Which value best describes the distance between home and school? Explain. 5a) mode:2 5b) median or mode: 2; mean is higher than most of the scores

19. CONFIDENTIAL 19 6) 21, 31, 26, 24, 28, 26 Use the data to make a box-and-whisker plot. 7) 12, 13, 42, 62, 62, 82 8) 2, 1, 3, 1, 2, 6, 2, 4 9) 104, 68, 90, 96, 101, 106, 95, 88

20. CONFIDENTIAL 20 A measure of central tendency describes how data clusters around a value. Data Distributions The mean is the sum of the values in the set divided by the number of values in the set. The median is the middle value when the values are in numerical order, or the mean of the two middle values if there are an even number of values. The mode is the value or values that occur most often. There may be one mode or more than one mode. If no value occurs more often than another, we say the data set has no mode. The range of a set of data is the difference between the least and greatest values in the set. The range describes the spread of the data. Let’s review

21. CONFIDENTIAL 21 Finding Mean, Median, Mode, and Range of a Data Set Find the mean, median, mode, and range of each data set. A) The number of hours Isaac did homework on six days: 3, 8, 4, 6, 5, 4. Write the data in numerical order. Add all the values and divide by the number of values. 3, 4, 4, 5, 6, 8 3_+ 4 + 4 + 5 + 6 + 8 6 mean: = 30 = 5 6

22. CONFIDENTIAL 22 4 occurs more often than any other value. median: The median is 4.5. 3, 4, 4, 5, 6, 8 There are an even number of values. Find the mean of the two middle values. mode: = 4 range: = 8 - 3 = 5

23. CONFIDENTIAL 23 A value that is very different from the other values in the set is called an outlier. In the data below, one value is much greater than the other values. This causes the mean to be greater than all of the other data values. In this case, either the median or mode would better describe the data.

24. CONFIDENTIAL 24 Choosing a Measure of Central Tendency Niles scored 70, 74, 72, 71, 73 and 96 on six geography tests. Use the mean, median, and mode of his scores to answer each question. mean = 76 median = 72.5 mode: none A) Which value gives Niles’ test average? The average of Niles’ scores is the mean, 76. B) Which value best describes Niles’ scores? Explain. The median score is the best description of Niles’ six scores. Most of his scores were near 72. The mean is higher than most of Niles’ scores because he scored 96 on one test. Since there is no mode, it is not a good description of the data.

25. CONFIDENTIAL 25 Measures of central tendency describe how data tends toward one value. You may also need to know how data is spread out across several values. Quartiles divide a data set into four equal parts. Each quartile contains one fourth of the values in the set. The inter quartile range (IQR) is the difference between the upper and lower quartiles. The IQR represents the middle half of the data.

26. CONFIDENTIAL 26 A box-and-whisker plot can be used to show how the values in a data set are distributed. The minimum is the least value that is not an outlier. The maximum is the greatest value that is not an outlier. You need five values to make a box-and-whisker plot: the minimum, first quartile, median, third quartile, and maximum.

27. CONFIDENTIAL 27 You did a great job today!