1. 6F Measuring the Spread of Data, 6G Box and Whisker Plots
Unit 2: Descriptive Statistics
6F, 6G
2/28/ :30 AM

2. Measures of Spread/Dispersion
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standard deviation all data range two pieces of data interquartile range (IQR) two (or four) pieces of data
6F, 6G
2/28/ :30 AM

3. Range
maximum minus the minimum data value A library surveys 20 borrowers each day from Monday to Friday, and records the number who are not satisfied with the range of reading material. The results are: 3, 7, 6, 8, 11 The following year the library receives a grant that enables the purchase of a large number of books. The survey is then repeated and the results are: 2, 3, 5, 4, 6 first survey = 8 second survey = 4 range is not a “resistant” measure of dispersion as it may be influenced by extreme values or outliers
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6F, 6G
2/28/ :30 AM

4. Interquartile Range (IQR)
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range of the middle half of the data upper quartile minus the lower quartile quartiles: includes the median; the two halves created by the median are then each divided in half to find the other two quartiles (used for 25th, 50th, and 75th percentiles) Example 1 n is odd 2, 2, 2, 3, 4, 4, 5, 6, 6, 7, 8 Example 2 n is even 10, 10, 11, 14, 15, 16, 17, 19, 21, 25
6F, 6G
2/28/ :30 AM

5. Fractiles
Quartiles Deciles Percentiles
6F, 6G
2/28/ :30 AM

6. Box-and-Whisker Plot
visual display of a data set’s five-number summary can be used to describe distribution (or compare sets of data) five-number summary: Minx, Q1, Q2, Q3, Maxx whiskers represent the top and bottom 25% of data box represents the middle 50% x
6F, 6G
2/28/ :30 AM

7. Outliers
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common test for outliers if the data contains outliers, plot outliers using asterisks and extend whiskers to the last value that is not an outlier boxplots with asterisks are referred to as “modified” boxplots
6F, 6G
2/28/ :30 AM

8. Describing Dispersion using Box-and-Whisker Plots
symmetric positively skewed negatively skewed
6F, 6G
2/28/ :30 AM

9. Examples
2, 2, 2, 2, 3, 3, 4, 5, 5, 5, 5, 6, 6, 6, 8, 16 Find the five-number summary and the IQR. Calculate the upper and lower bounds and determine if the data contains outliers. Draw a number line with an even interval using a straight edge. Construct the box and whiskers. Mark any outliers with an asterisk. Describe the distribution of the data. Determine the value at the 75th percentile. Use a calculator to check all of your work. 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 Find the five-number summary.
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6F, 6G
2/28/ :30 AM

10. How can it be done using a calculator?
Example
A hospital is trialing a new anesthetic drug and has collected data on how long the new and old drugs take before the patient becomes unconscious. They wish to know which drug acts faster and which is more reliable.
old drug times: 8, 12, 9, 8, 16, 10, 14, 7, 5, 21, 13, 10, 8, 10, 11, 8, 11, 9, 11, 14
new drug times: 8, 12, 7, 8, 12, 11, 9, 8, 10, 8, 10, 9, 12, 8, 8, 7, 10, 7, 9, 9
Prepare parallel boxplots for the data sets and use it to compare the two drugs for speed and reliability.
How can it be done using a calculator?
6F, 6G
2/28/ :30 AM