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Pre-test and Warm-up

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Practice At East Hall high school for physical fitness week all the ninth graders height was measured in inches and written down. The following lists are for the ninth grade boys and the ninth grade girls. Boys: 59, 60, 61, 61, 62, 63, 63, 65, 66, 66, 66, 67, 68, 70, 72 Girls: 49, 50, 51, 52, 53, 53, 56, 58, 59, 70, 75 1. Find the range of both sets of data (boys and girls). Which has a larger range? 2. Find the mean and the median of the boys heights. Which one best describes the average height of the boys? why? 3. Find the mean and the median of the girls heights. Which one best describes the average height of girls? why?

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Mean and Medians are both ways to find the “central middle” of a set of data. However, they are each “the best” at different times. As you saw in the problems earlier the boys mean and medians were relatively close. This is because the boys heights were evenly spread out. In this case mean is the best way to tell what the middle of the heights are because it is slightly more accurate. The girls, on the other hand, had a median that was significantly lower than the mean. This is because 2 of the girls heights were much taller than the rest. In this case the median is the best way to tell what the middle of the heights are because it is unaffected by the 2 extremely tall girls (outliers). Rule: Whenever the data has an outlier the better measure of the middle is the median, because the median is unaffected by outliers. However, if there are no outliers than the better measure of the middle is the mean, because it more accurately represents all the data.

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Warm-Up The following are test grades for Mr. Hoyt’s algebra class: 100, 78, 95, 33, 88, 91 1. Find the mean and the median of the data above. 2. Which one (the mean or the median) is the better measure of central tendency in this problem? Why?

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X X - ̅ x Absolute Value 11 5 7 5 6 10 12

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Video and Practice finding MAD http://www.youtube.com/watch?v=z9AJk7TvdpQ http://www.youtube.com/watch?v=z9AJk7TvdpQ Find the mean absolute deviation for each data set below 1) 5, 9, 11, 4, 12, 15, 72) 12, 8,9,4,3,2,4 3)8,9,7,11,17,15,104)14,6,5,15,9,11,3

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Warm-up 3) This table shows admission price for various museums in the same city. Museum Prices: $9.00 $12.00 $9.75 $8.25 $11.25 Which is the mean absolute deviation for this set of data?

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Quartiles A quartile is a type of median of an ordered set of data. However it is not the middle number like a median is. If you divide a set of data in half (a upper half, and a lower half) the upper quartile is simply the median or middle of the upper half of data, and the lower quartile is the median or middle of the lower half of data. Example: Looks at the data set: 22,23,24,25,26,27,27,27,28,30,31 Interquartile Range (IQR) is Q3 – Q1 In the problem above the IQR is 28-24=4 Median Lower Half Upper Half Q1 Lower Quartile Q3 Upper Quartile

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http://www.youtube.com/watch?v=WYxtE1Q6_GE http://www.youtube.com/watch?v=WYxtE1Q6_GE For 1 and 2 Find the Q1, Q3, and IQR 1)41, 37, 58, 62, 46, 33, 74, 51, 69, 81, 55 2) 182, 149, 172, 161, 68, 179, 142, 187, 170, 155 3) Using the data from #2 you will find the MAD is 22.8. Compare this with the IQR you got in #2. Which one (IQR or MAD) best describes the spread of the data? Why?

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Day123456 Texts Sent 908576698184 Texts Received 887778748186 Which Conclusion is NOT true? a)The interquartile range of the texts is the same for both sent and received. b)The lower quartile for the text sent is lower than the lower quartile for text received. c)The mean and median of texts sent were higher than the mean and median for texts received. d)The upper quartile for the text received was lower than the upper quartile for texts sent.

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The five number summary is made up of the minimum, Q1, Median, Q3, and Maximum values. Box and whiskers plot is a graph of the 5 number summary. Example: Find the 5 numbers Sum, The IQR, and make a box and whiskers plot for the data: 42, 42, 44, 45, 46, 46, 48, 49, 52, 53, 56 Min Q1 Med Q3 Max 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56

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When comparing multiple box plots to decide which one has the highest or lowest average you want to look the 5 number summary of each plot to see how they compare. Here class 1 is ALL relatively small compared to the other boxes. It has the lowest max, the 2 nd lowest Q3 and 2 nd lowest median and the 2 nd lowest Q1. All of the other box plots have significantly higher Maxes and Q3s.

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Practice: Create a box and Whiskers plot for the following problems. 1. 11, 16, 18, 17, 20, 10, 14, 10, 17, 12, 15 2. 10, 63, 52, 40, 8, 12, 73, 49, 26, 57, 32, 19 10 11 12 13 14 15 16 17 18 19 20 10 20304050607080

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Practice EOCT Questions

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6-9 Data Distributions Objective Create and interpret box-and-whisker plots.

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