First Quartile = 26 Third Quartile = 35 Interquartile Range = 9

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1 Lesson 9.4 Name: Quartile The quartiles of a set of data divide the data into 4 equal parts. First Quartile The first quartile of a set of data is the median of the lower half of the data. Median The median of a set of data is the number that falls in the middle of the data when numbers are arranged least to greatest. The median is also called the Second Quartile. Third Quartile The third quartile of a set of data is the median of the upper half of the data. Interquartile Range The interquartile range of data is the difference between the first and third quartiles of the data. Example lower half upper half First Quartile = 14.5 Third Quartile = 25 Interquartile Range = 10.5 Example 2 NOTE: When you have an odd amount of numbers like the set below, the median (31) is not included in the lower OR upper half of data when finding quartiles lower half upper half First Quartile = 26 Third Quartile = 35 Interquartile Range = 9 NOTE: The quartiles divide the data into 4 parts. The first part is between the smallest value and the first quartile. The second part is between the first quartile and the median (second quartile). The third part is between the median and the third quartile. And the fourth part is between the third quartile and the highest value.

2 9.4 HW Name: Data Set 1 (REMEMBER Don t include the median in the lower or upper half) 23, 21, 29, 22, 28, 25, 27 (least to greatest) 1) First Quartile = 2) Median = 3) Third Quartile = 4) Interquartile Range = 5) Range = Data Set 2 14, 9, 19, 11, 8, 7, 21, 17 (least to greatest) 6) First Quartile = 7) Median = 8) Third Quartile = 9) Interquartile Range = 10) Range =

3 Lesson 9.5 Name: Mean Absolute Deviation (MAD) The mean absolute deviation is the average of how much data values differ from the mean. Example 1 You record the numbers of raisins in 8 scoops of cereal. Find the record the mean absolute deviation of the data. Data Set: 1, 2, 2, 2, 4, 4, 4, 5 Step 1: Find the mean. Sum of the data is 24. Divide 24 by 8 to get 3. The mean is equal to 3. Step 2: Record how far each piece of data is from the mean. 2, 1, 1, 1, 1, 1, 1, 2 The 2 is how far 1 is from the mean. The 3 2 s and 3 4 s are all 1 from the mean so that s where the 6 1 s come from. And the 5 is 2 from the mean, which is where the final 2 comes from. Step 3: Find the sum of these distances from the mean. They add up to 10. Step 4: Take the sum in step 3 and make it the numerator in a fraction. The denominator is the number of data pieces, which is 8. So the fraction is: 10 8 Convert the fraction to a decimal: 1.25 So, the data values differ from the mean by an average of 1.25 raisins. Example 2 Test Scores: 85, 80, 66, 95, 88 Mean = 82.8 Each data value s distance from mean: 2.2, 2.8, 16.8, 12.2, 5.2 Sum of distances = 39.2 Fraction of distances compared to number of values: Convert to decimal: 7.84 So the values differ from the mean by an average of 7.84 points. The Mean Absolute Deviation = 7.84

4 9.5 HW Name: Find the MEAN ABSOLUTE DEVIATION for each data set below: Use your notes Use a calculator 1) Coastal Plains High School had six home football games this season. The set of data below shows how many points they scored in each game Find the MEAN ABSOLUTE DEVIATION of their point totals. Mean = Distances from mean: Sum of distances = Fraction of sum of distances/number of values = MEAN ABSOLUTE DEVIATION = (rounded to nearest tenths) 2) There were 5 major snowstorms in New York City last year. The set of data below shows the number of inches of snow each storm brought Find the MEAN ABSOLUTE DEVIATION of the snow amounts. Mean = Distances from mean: Sum of distances = Fraction of sum of distances/number of values = MEAN ABSOLUTE DEVIATION = (rounded to nearest tenths)

Review Packet for Test 8 - Statistics. Statistical Measures of Center: and. Statistical Measures of Variability: and.

Name: Teacher: Date: Section: Review Packet for Test 8 - Statistics Part I: Measures of CENTER vs. Measures of VARIABILITY Statistical Measures of Center: and. Statistical Measures of Variability: and.