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3-3 Measures of Variation Day 1

3-3 Measures of Variation Day 1. Discussion. We know to use the mean when the data is close together. What does close together mean? In statistics, the way data is spread out is called distribution. This can easily been seen on a graph. Discussion.

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3-3 Measures of Variation Day 1

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  1. 3-3 Measures of VariationDay 1

  2. Discussion We know to use the mean when the data is close together. What does close together mean? In statistics, the way data is spread out is called distribution. This can easily been seen on a graph.

  3. Discussion Using your own words, describe the distribution of each data set.

  4. Discussion In statistics, we use values to describe how data is distributed (spread out). These values are called variation. Today we will just use words to describe how the data is distributed. In the days to come, we will learn these values of variation.

  5. Discussion Class Grades: 62, 65, 94, 95, 95, 96 The average grade is 85%. Does the average tell the entire story? The class grades has a distribution that is close together with two outliers. Does the distribution summarize the data better?

  6. Discussion The mean and median tell you about the middle of the data set and the variation explains how the data is spread out. Both statistics (measures of center and variation) are valuable because they help to summarize the data.

  7. Definitions Variation – value used to describe the distribution of the data What does distribution mean? How the data is spread out What does the mean and median describe? Center of the data Notice how these two values are different.

  8. Definitions Today we are just going to use words to describe the distribution of the data set. Here are the words that we are going to use: Normal - close together Normal w/ an outlier - close together w/ an outlier Random - spread out

  9. Example 1: Class Grades Put 1 finger up if you think the distribution is normal, 2 if you think it’s random, and 3 if you think it’s normal with outliers. Period 1: 58, 62, 85, 88, 90, 93, 93, 95, 97, 98 Period 2: 78, 80, 80, 81, 83, 84, 84, 86, 88, 90 Period 3: 25, 40, 55, 70, 72, 74, 80, 98, 98, 99

  10. 3-3 Measures of VariationDay 2

  11. Today’s Objective You will be able tocalculate different statistical values to describe distribution.

  12. Definition Range– difference between the highest and lowest data values What would a range of 5 mean? Data close together What would a range of 100 mean? Data far apart or outlier

  13. Definition Quartile– values that divide data into four parts Interquartile Range (IQR)–difference between the 1st and 3rd quartiles What does a small/large IQR mean? Data close/far in the middle 50%

  14. Definition The range will tell us how far apart the data is from beginning to end. The Interquartile Range (IQR) will tell us how far apart the data is in the middle.

  15. How to Find IQR: 1. Order the data from least to greatest. 2. Find the median. 3. Calculate the median of both the lower and upper half of the data. 4. The IQR is the difference between the upper and lower medians.

  16. Example 1 Find the range and IQR. Period 1 Grades: 58, 62, 72, 85, 93, 93, 95, 97, 98

  17. Example 1 Find the range and IQR. Period 1 Grades: 58, 62, 72, 85, 93, 93, 95, 97, 98 Range = 98-58 = 40 IQR: Order (done) Median: 93 Median of lower half (58,62,72,85)= 67 Median of upper half (93,95,97,98)= 96 4. IQR= 96 – 67 = 29

  18. Example 2 Find the range and IQR. Period 2 Grades: 78, 80, 81, 83, 84, 84, 88, 90

  19. Example 2 Find the range and IQR. Period 2 Grades: 78, 80, 81, 83, 84, 84, 88, 90 Range: 12 IQR: 5.5

  20. You Try! Find the mean, median, range, and IQR. Then describe the distribution. 1. 10, 12, 14, 18, 20, 22, 24 2. 22, 24, 24, 28, 30, 32, 34, 90

  21. What did we learn today? Tocalculate different statistical values to describe distribution

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