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Section 13.4/13.5 MEASURES OF SPREAD

Section 13.4/13.5 MEASURES OF SPREAD. Measures of spread or variability is another way to compare data. Percentile Ranking : If a student is in the 75 th percentile, it means that the student finished higher than 75% of all the other students. For example, if scores on a test were as follows:

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Section 13.4/13.5 MEASURES OF SPREAD

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  1. Section 13.4/13.5 MEASURES OF SPREAD

  2. Measures of spread or variability is another way to compare data

  3. Percentile Ranking: If a student is in the 75th percentile, it means that the student finished higher than 75% of all the other students For example, if scores on a test were as follows: 2, 3, 5, 6, 7, 7, 8, 9, 9 ,11, 15, 20 To calculate the 75th percentile 75% of 12 scores = 9 scores The 75th percentile is the 9th score from the bottom Therefore the 75th percentile score is 9

  4. Quartiles When data is arranged in order from least to greatest, the median is the middle number in the set of data. Quartiles represent the data items that are one quarter and three quarters of the way through a set of data For example, consider the set of data 1, 2, 3, 4, 5, 6, 7, 8, 9 Upper quartile Q3 7.5 Lower quartile Q1 2.5 Median 5

  5. We can approximate the quartiles and the median using a cumulative frequency polygon Q377 Median 72 Q164

  6. The median and the upper and lower quartiles are often displayed using a BOX PLOT Minimum value 48 Maximum value 90 Median = 72.5 Q3= 77 Q1= 65 Interquartile range Q3-Q1=77-65=12

  7. Another measure of variability is Deviation from the mean Total = 15.6 Mean deviation = 15.6/5 = 3.12

  8. Standard Deviation The average of the squares of the deviation from the mean is called the Variance. This is a difficult formula to use

  9. We can rearrange the formula

  10. Therefore the Variance is The Standard Deviation is the square root of the variance

  11. Example 1:Scores on a geometry test are recorded in the table below

  12. a) Determine the mean, median, and mode for the data b) Determine the upper and lower quartile for the data c) Determine the standard deviation for the data d) Display the data using a frequency histogram e) Display the data using a box plot

  13. mean Standard deviation Lower quartile upper quartile Mode = 24

  14. HOMEWORK: PAGE 481 # 1, 2 PAGE 485 # 4, 5

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