1. Unit 4: Probability Day 4: Measures of Central Tendency and Box and Whisker Plots

2. Standards and Benchmarks 9.4.1.1 Describe a data set using data displays, including box-and-whisker plots; describe and compare data sets using summary statistics, including measures of center, location and spread. Measures of center and location include mean, median, quartile and percentile.

3. Learning Targets a) I can describe data sets using box-and- whisker plots. b) I can use measures of center (mean, median) to describe and compare data sets. c) I can use measures of spread (range, IQR, standard deviation) to describe and compare data sets.

4. Measures of Central Tendency and Box and Whisker Plots Recall that the mean, median, and mode are measures of central tendency—values that describe the center of a data set. The mean is the sum of the values in the set divided by the number of values (the average) The median is the middle value or the mean of the two middle values when the set is ordered numerically. The mode is the value or values that occur most often. A data set may have one mode, no mode, or several modes.

5. Measures of Central Tendency and Box and Whisker Plots Ex. Find the mean, median, and mode of the data. Deer at a feeder each hour: 3, 0, 2, 0, 1, 2, 4 Mean: Median: Mode:

6. Measures of Central Tendency and Box and Whisker Plots Ex. Find the mean, median, and mode of the data set: {6, 9, 3, 8} Mean: Median: Mode:

7. Measures of Central Tendency and Box and Whisker Plots A box-and-whisker plot shows the spread of a data set. It displays 5 key points: the minimum and maximum values, the median, and the first and third quartiles. NOTE: IQR = Q3 – Q1

8. Measures of Central Tendency and Box and Whisker Plots Special Note: The quartiles (Q1 and Q3) are the medians of the lower and upper halves of the data set. If there are an odd number of data values, do not include the median in either half. The interquartile range, or IQR, is the difference between the 1st and 3rd quartiles, or Q3 – Q1. It represents the middle 50% of the data.

9. Measures of Central Tendency and Box and Whisker Plots Make a box-and-whisker plot of the data. Find the interquartile range. {6, 8, 7, 5, 10, 6, 9, 8, 4}

10. Measures of Central Tendency and Box and Whisker Plots Make a box-and-whisker plot of the data. Find the interquartile range. {13, 14, 18, 13, 12, 17, 15, 12, 13, 19, 11, 14, 14, 18, 22, 23}

11. Measures of Central Tendency and Box and Whisker Plots Group Time: Statistics Poster Project Work Time: WKST 11-5 Practice B

12. Measures of Central Tendency and Box and Whisker Plots Exit Quiz: Use the data set {9, 4, 7, 8, 5, 8, 18, 5} for questions #1 - #2 1. Find the mean, median, and mode. Mean: _____ Median: _____ Mode: _____ 2. Make a box-and-whisker plot of the data. Find the interquartile range. IQR: _____