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5 Minute Check Complete on the back of your homework. 1. The number of songs downloaded per month by a group of friends were 8,12,6,4,2,0, and 10. Find.

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Presentation on theme: "5 Minute Check Complete on the back of your homework. 1. The number of songs downloaded per month by a group of friends were 8,12,6,4,2,0, and 10. Find."— Presentation transcript:

1 5 Minute Check Complete on the back of your homework. 1. The number of songs downloaded per month by a group of friends were 8,12,6,4,2,0, and 10. Find the measure of center that best represents the data. 2. The ages of participants in a relay race are 12,15,14,13,15,12, 22,16, and 11. Identify the outlier in the data set. Determine how the outlier affects the mean, median, and mode. Tell which measure of center best describes the data with and without the outliers.

2 5 Minute Check Complete on the back of your homework. 1. The number of songs downloaded per month by a group of friends were 8,12,6,4,2,0, and 10. Find the measure of center that best represents the data.

3 5 Minute Check Complete on the back of your homework. 1. The number of songs downloaded per month by a group of friends were 8,12,6,4,2,0, and 10. Find the measure of center that best represents the data. Since the data set has no outliers or repeated values, the mean or median would be the best. Mean = 6 Median = 6

4 5 Minute Check Complete on the back of your homework. 2. The ages of participants in a relay race are 12,15,14,13,15,12,22,16, and 11. Identify the outlier in the data set. Determine how the outlier affects the mean, median, and mode. Tell which measure of center best describes the data with and without the outliers.

5 5 Minute Check Complete on the back of your homework. 2. The ages of participants in a relay race are 12,15,14,13,15,12,22,16, and 11. Identify the outlier in the data set. Determine how the outlier affects the mean, median, and mode. Tell which measure of center best describes the data with and without the outliers. Outlier is 22. Without OutlierWith Outlier Mean 13.5Mean 14.4 Median 13.5Median 14 Mode 12 &15Mode 12 & 15 The mode best describe the data because it does not change with the outlier.

6 Tuesday, March 24 Chapter 6.11.3 Measures of Variation

7 Objective: To find the measure of variation in a data set.

8 Measures of Variation Measures of variation is used to describe the distribution, or spread, of the data.

9 Measures of Variation Measures of variation include: Range 1 st and 3 rd Quartiles (Q ₁ and Q ₃ ) Interquartile Range (IQR)

10 Measures of Variation Find the measures of variation for the data set. 5, 8, 4, 4, 9, 6, 3, 8, 7 How to find the Measures of Variation Put the data set in order from least to greatest.

11 Measures of Variation Find the measures of variation for the data set. 5, 8, 4, 4, 9, 6, 3, 8, 7 3, 4, 4, 5, 6, 7, 8, 8, 9 How to find the Measures of Variation Put the data set in order from least to greatest.

12 Measures of Variation Find the measures of variation for the data set. 5, 8, 4, 4, 9, 6, 3, 8, 7 3, 4, 4, 5, 6, 7, 8, 8, 9 Range Subtract the least number from the greatest number in the data set.

13 Measures of Variation Find the measures of variation for the data set. 5, 8, 4, 4, 9, 6, 3, 8, 7 3, 4, 4, 5, 6, 7, 8, 8, 9 Range: 9-3=6 Range Subtract the least number from the greatest number in the data set. Range:6

14 Measures of Variation Find the measures of variation for the data set. 5, 8, 4, 4, 9, 6, 3, 8, 7 3, 4, 4, 5, 6, 7, 8, 8, 9 1 st quartile. Step 1 - Circle the bottom half of numbers. If there is a single median, do not include. Range:6

15 Measures of Variation Find the measures of variation for the data set. 5, 8, 4, 4, 9, 6, 3, 8, 7 3, 4, 4, 5, 6, 7, 8, 8, 9 single median 1 st quartile. Step 1 - Circle the bottom half of numbers. If there is a single median, do not include. Range:6

16 Measures of Variation Find the measures of variation for the data set. 5, 8, 4, 4, 9, 6, 3, 8, 7 3, 4, 4, 5, 6, 7, 8, 8, 9 1 st quartile. Step 2 - Find the middle number, or an average of the two middle numbers in the circle. Range:6

17 Measures of Variation Find the measures of variation for the data set. 5, 8, 4, 4, 9, 6, 3, 8, 7 3, 4, 4, 5, 6, 7, 8, 8, 9 1 st quartile. Step 2 - Find the middle number, or an average of the two middle numbers in the circle. Range:6 1 st Q: 4

18 Measures of Variation Find the measures of variation for the data set. 5, 8, 4, 4, 9, 6, 3, 8, 7 3, 4, 4, 5, 6, 7, 8, 8, 9 3rd quartile. Step 1 - Circle the top half of numbers. Range:6 1 st Q: 4

19 Measures of Variation Find the measures of variation for the data set. 5, 8, 4, 4, 9, 6, 3, 8, 7 3, 4, 4, 5, 6, 7, 8, 8, 9 3rd quartile. Step 1 - Circle the top half of numbers. Range:6 1 st Q: 4

20 Measures of Variation Find the measures of variation for the data set. 5, 8, 4, 4, 9, 6, 3, 8, 7 3, 4, 4, 5, 6, 7, 8, 8, 9 3rd quartile. Step 2 - Find the middle number, or an average of the two middle numbers in the circle. Range:6 1 st Q: 4

21 Measures of Variation Find the measures of variation for the data set. 5, 8, 4, 4, 9, 6, 3, 8, 7 3, 4, 4, 5, 6, 7, 8, 8, 9 3rd quartile. Step 2 - Find the middle number, or an average of the two middle numbers in the circle. Range:6 1 st Q: 4 3 rd Q: 8

22 Measures of Variation Find the measures of variation for the data set. 5, 8, 4, 4, 9, 6, 3, 8, 7 3, 4, 4, 5, 6, 7, 8, 8, 9 Interquartile Range. Subtract Q 1 from Q 3. Range:6 1 st Q: 4 3 rd Q: 8

23 Measures of Variation Find the measures of variation for the data set. 5, 8, 4, 4, 9, 6, 3, 8, 7 3, 4, 4, 5, 6, 7, 8, 8, 9 8 – 4 = 4 Interquartile Range. Subtract Q 1 from Q 3. Range:6 1 st Q: 4 3 rd Q: 8 IQR: 4

24 Measures of Variation Find the measures of variation for the data set. What do we do first?

25 Measures of Variation Find the measures of variation for the data set. 1, 8, 25, 30, 50, 70 Range? Range: Q ₁ : Q ₃ : IQR:

26 Measures of Variation Find the measures of variation for the data set. 1, 8, 25, 30, 50, 70 70 – 1 = 69 Q1? Range:69 Q ₁ : Q ₃ : IQR:

27 Measures of Variation Find the measures of variation for the data set. 1, 8, 25, 30, 50, 70 Q3? Range:69 Q ₁ : 8 Q ₃ : IQR:

28 Measures of Variation Find the measures of variation for the data set. 1, 8, 25, 30, 50, 70 IQR? Range:69 Q ₁ : 8 Q ₃ : 50 IQR:

29 Measures of Variation Find the measures of variation for the data set. 1, 8, 25, 30, 50, 70 50 – 8 = 42 Range:69 Q ₁ : 8 Q ₃ : 50 IQR:42

30 Measures of Variation An outlier is a data value that is either much greater or less than the median.

31 Measures of Variation An outlier is a data value that is either much greater or less than the median. An outlier is more than 1.5 times the IQR

32 Measures of Variation Find the measures of variation for the data set. 1, 8, 25, 30, 50, 70 To Find an Outlier Step 1 – Multiply the IQR by 1.5. Range:69 Q ₁ : 8 Q ₃ : 50 IQR:42

33 Measures of Variation Find the measures of variation for the data set. 1, 8, 25, 30, 50, 70 42 · 1.5 = 63 To Find an Outlier Step 1 – Multiply the IQR by 1.5. Range:69 Q ₁ : 8 Q ₃ : 50 IQR:42

34 Measures of Variation Find the measures of variation for the data set. 1, 8, 25, 30, 50, 70 42 · 1.5 = 63 To Find an Outlier Step 2 – Subtract this from Q ₁ and add to Q ₃. Range:69 Q ₁ : 8 Q ₃ : 50 IQR:42

35 Measures of Variation Find the measures of variation for the data set. 1, 8, 25, 30, 50, 70 8 - 63 = -55 50 + 63 = 113 To Find an Outlier Step 2 – Subtract this from Q ₁ and add to Q ₃. Range:69 Q ₁ : 8 Q ₃ : 50 IQR:42

36 Measures of Variation Find the measures of variation for the data set. 1, 8, 25, 30, 50, 70 8 - 63 = -55 50 + 63 = 113 To Find an Outlier Step 3 – Determine if any numbers in the data set are outside this range. Range:69 Q ₁ : 8 Q ₃ : 50 IQR:42

37 Measures of Variation Find the measures of variation for the data set. 1, 8, 25, 30, 50, 70 8 - 63 = -55, No 50 + 63 = 113, No To Find an Outlier Step 3 – Determine if any numbers in the data set are outside this range. Range:69 Q ₁ : 8 Q ₃ : 50 IQR:42

38 Measures of Variation The lengths of various bridges are 88, 345, 867, 251, 546,1903 and 274 feet. Find the measures of variation and any outliers.

39 Measures of Variation The lengths of various bridges are 88, 345, 867, 251, 546,1903 and 274 feet. Find the measures of variation and any outliers. 88, 251, 274, 345, 546, 867,1903 Range: 1903-88 = 1815 Range: 1815 Q ₁ : Q ₃ : IQR: Outlier:

40 Measures of Variation The lengths of various bridges are 88, 345, 867, 251, 546,1903 and 274 feet. Find the measures of variation and any outliers. 88, 251, 274, 345, 546, 867,1903 Q ₁ : 251 Range: 1815 Q ₁ : 251 Q ₃ : IQR: Outlier:

41 Measures of Variation The lengths of various bridges are 88, 345, 867, 251, 546,1903 and 274 feet. Find the measures of variation and any outliers. 88, 251, 274, 345, 546, 867,1903 Q ₃ : 867 Range: 1815 Q ₁ : 251 Q ₃ : 867 IQR: Outlier:

42 Measures of Variation The lengths of various bridges are 88, 345, 867, 251, 546,1903 and 274 feet. Find the measures of variation and any outliers. 88, 251, 274, 345, 546, 867,1903 IQR: 867-251=616 Range: 1815 Q ₁ : 251 Q ₃ : 867 IQR: 616 Outlier:

43 Measures of Variation The lengths of various bridges are 88, 345, 867, 251, 546,1903 and 274 feet. Find the measures of variation and any outliers. 88, 251, 274, 345, 546, 867,1903 Outliers: 616 x 1.5 = 924 251-924 and 867+924 - 673 to 1791 Range: 1815 Q ₁ : 251 Q ₃ : 867 IQR: 616 Outlier: 1903

44 Measures of Variation Temperatures for the first half of the year are given for two cities. Compare and contrast the measures of variation of the two cities. Do this on your own.

45 Measures of Variation Temperatures for the first half of the year are given for two cities. Compare and contrast the measures of variation of the two cities. The Q1, Q3 and IQR are similar, but the range is more spread out in the Antelope data. MT ME Range: 5847 Q ₁ : 3032 Q ₃ : 7066 IQR: 4034 Outlier: nonenone

46 Measures of Variation The double stem and leaf plot shows the high temperatures for two cities in the same week. Compare and contrast the measures of variation of the two cities. Do this on your own.

47 Measures of Variation The double stem and leaf plot shows the high temperatures for two cities in the same week. Compare and contrast the measures of variation of the two cities. The Minneapolis temperatures are closer together than the Columbus temperatures. Minn Col Range: 2337 Q ₁ : 2127 Q ₃ : 3648 IQR: 1521 Outlier: nonenone

48 PARCC 9

49

50 PARCC EXTRA How many square cubes with a side dimension of 1/2 in will fit in the box below? 5in 4 in 6 in

51 PARCC EXTRA How many square cubes with a side dimension of 1/2 in will fit in the box below? 5in 4 in 6 in 12 cubes 8 cubes 10 cubes 12 x 8 x 10 = 960 cubes

52 PARCC EXTRA How many square cubes with a side dimension of 1/2 in will fit in the box below? 5in 4 in 6 in 6 x 4 x 5 = 120 in² There are 8 cubes in one sq in. 120 x 8 = 960 cubes

53 Measures of Variation Agenda Notes Homework– Homework Practice 6.11.3 Due Wednesday, March 25 Chapter 6.11 Test Friday, March 27

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