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Warm Up

Warm Up. What is the spread of the data set below? 21, 53, 11, 19, 50, 8, 5, 25 Given the following list of Math test scores, create a frequency table with at least 5 groupings. Then make a histogram & label! 55, 94, 82, 99, 68, 76, 89, 92, 88, 95, 87,91. HW Check 2.2.

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Warm Up

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  1. Warm Up • What is the spread of the data set below? 21, 53, 11, 19, 50, 8, 5, 25 • Given the following list of Math test scores, create a frequency table with at least 5 groupings. Then make a histogram & label! 55, 94, 82, 99, 68, 76, 89, 92, 88, 95, 87,91

  2. HW Check 2.2

  3. Unit 2, Day 3Boxplots

  4. Boxplots Min Q1 Median Q3 Max Lower Upper Quartile Quartile Each quartile represents 25% of the data

  5. Five-number Summary • Used to construct a box-and-whisker plot • Minimum – smallest value of the data set • Maximum – largest value of the data set • Median – middle value of the data set • Quartile 1 (Q1) – median of the lower data points • Quartile 3 (Q3) – median of the upper data points

  6. Boxplots Min Q1 Median Q3 Max Lower Upper Quartile Quartile The Interquartile Range (IQR) is the spread of the middle 50% of the data. It is represented by the length of the box.

  7. Example: Box Plot Use this set of data to make a Box Plot… 59, 27, 18, 78, 61, 91, 52, 34, 54, 93, 100, 87, 85, 82, 68

  8. Boxplots on the Calculator What’s the difference?

  9. Is it an outlier? 1st – calculate IQR 2nd – calculate 1.5*IQR 3rd – a number is an outlier if it is greater then Q3 + 1.5*IQR or if it is less then Q1 – 1.5*IQR

  10. Box Plot & Histogram of the same data

  11. Determine if there are any outliers in the following set of data 10.2,  14.1,  14.4.   14.4,  14.4,  14.5,  14.5,  14.6,  14.7,  14.7,  14.7,  14.9,  15.1,  15.9,   16.4

  12. Interpreting Measures of Spread • Range: max – min; spread of the entire data set – sensitive to outliers • IQR: Q3 – Q1; spread of the middle 50% of the data – not sensitive to outliers • Standard Deviation: the typical amount that a data value will vary from the mean – sensitive to outliers

  13. How do you decide whether to use the mean and standard deviation or the median and IQR to summarize the data numerically? Outliers

  14. Practice! Below is a stem and leaf plot of the amount of money spent by 25 shoppers at a grocery store. Key: 42 = $42

  15. Practice! • Calculate the mean and median. • Calculate the lower and upper quartiles and IQR. • Determine which, if any, values are outliers. • Write several sentences to describe this data set in context. • Name some factors that might account for the extreme values, and the much lower measure of center. Key: 42 = $42

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