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Box and Whisker.notebook
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April 10, 2014
measures of variability
box-and-whisker plots
Ch. 14 Lesson 3
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Measure of Variability - A number that represents the spread (or the diversity) of a set of data
**The larger the measure of variability, the more the data is spread out
Range: Difference between the two extremes
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Breaking Data into Quartiles:
Quartiles - Four groupings of a set of data determined by the median of the set and the medians of the sets determined by the median
1) List all data values in order from least to greatest and find
the median (Q2)
2) Take the first half of the data and find the median of that set *That median is called Q1
3) Find the median of the second half set of data*That median is called Q3
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Interquartile Range (IQR)
The difference between Q3 and Q1
IQR = Q3 - Q1
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Example 1) Find the interquartile range of the college enrollments listed below:
10,548 13,962 15,863 6,285 16,473 18,473 19,871 20,945 22,434 23,488 27,507 32,874 35,116
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Box-and-Whisker Plots
- Made up of a rectangular box with the ends at Q1 and Q3
- The box has a vertical bar separating it at Q2
- Segments (whiskers) extend from the ends of the box*Whiskers extend to the minimum and maximum values unless there exists an outlier(s) in the data
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Box-and-Whisker Plots
Outlier - Any value that is more than 1.5 times the IQR beyond Q1 and Q3
Outlier < Q1 - 1.5(IQR) OR Outlier > 1.5(IQR) + Q3
***If outliers exist, the whisker extends to the last data value that is not an outlier
555555 555 95
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Example 2) Use the data from Example 1 to draw a box-and-whisker plot
10,548 13,962 15,863 16,285 16,473 18,473 19,871 20,945 22,434 23,488 27,507 32,874 35,116
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Example 3) Find the minimum, maximum, Q1, Q2, Q3, and any outliers in the set of data. Then draw a box-and-whisker plot for the provided set of data
{7, 1, 11, 5, 4, 8, 12, 58, 15, 9, 6, 5, 9}
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Example 4) Find the minimum, maximum, Q1, Q2, Q3, and any outliers in the set of data. Then draw a box‐and‐whisker plot for the provided set of data
{21, 24, 10, 13, 26, 19, 1, 5, 12, 6}
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Example 5) Use the boxandwhisker plot to answer the questions:
a) What are the maximum and minimum values?
b) What are the values of Q1, Q2, and Q3?
c) Are there any outliers? If so, what are they?
d) What is the IQR and the overall range of the data?
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Use the boxandwhisker plot to answer the questions:
a) What are the maximum and minimum values?
b) What are the values of Q1, Q2, and Q3?
c) Are there any outliers? If so, what are they?
d) What is the IQR and the overall range of the data?
Evaluation:
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