6-5 Describing Distributions I CAN describe the shape of data distributions of a dot plot. I CAN describe the shape of data distributions of a box-and-whisker plot. I CAN make conclusions about data displayed on two box-and-whisker plots.

6-5 Describing Distributions Recall that a frequency distribution is a display that shows how many times data values fall into categories of quantity. Frequency distributions are categorized by their general shape. Skewed Normal Data is not symmetric about the center. Data is symmetric about the center. The measures of center may not be equal. The measures of center are equal. Shapes of a Distribution

6-5 Describing Distributions Example 1: Displaying Distributions on Dot Plots A. The data set and dot plot display heart rate data. Describe the shape of the data distribution. 85, 84, 83, 82, 85, 80, 84, 90, 87, 85, 86, 88, 86, 85 The data is symmetrical about the center. The mean, median, and mode are equal. It shows a normal shape of distribution.

6-5 Describing Distributions Continued: Example 1 B. The data set and dot plot display students’ quiz scores. Describe the shape of the data distribution. 10, 8, 7, 9, 10, 9, 9, 7, 8, 9, 6, 8 The data is not symmetrical about the center. The mean, median, and mode are different. It shows a skewed shape of distribution.

6-5 Describing Distributions You Try! Example 1 The data set and dot plot display the number of miles Danny ran each day. Describe the shape of the data distribution. The data is not symmetrical about the center. The mean, median, and mode are different. It shows a skewed shape of distribution.

6-5 Describing Distributions Example 2: Displaying Distributions on Box-and- Whisker Plots The data set and box-and-whisker plot display the weights in kilograms of 12 cats. Describe the shape of the data distribution. 5, 2, 6, 4, 6, 3, 4, 9, 3, 5, 3, 4 The shape of the data distribution is skewed.

6-5 Describing Distributions You Try! Example 2 The box-and-whisker plot shows the ages of the 20 boys and girls at Ella’s birthday party. Describe the shape of the data distribution. The shape of the data distribution is normal.

6-5 Describing Distributions Example 3: Comparing Distributions using Box- and-Whisker Plots The box-and-whisker plots show the distribution of cars sold each day on two lots in a month. What conclusions can you make about the data? In general, more cars were sold each day in Lot A than in Lot B. The spread of the data is greater for Lot B, which means that there is more variation in the data. The number of cars sold in Lot A is more predictable than the number of cars sold in Lot B.

6-5 Describing Distributions You Try! Example 3 The box-and-whisker plots show the distribution of cars sold each day on two lots in a month. What conclusions can you make about the data? In general, more cars were sold each day in Lot B than in Lot A. The spread of the data is greater for Lot B, which means that there is more variation in the data. The number of cars sold in Lot A is more predictable than the number of cars sold in Lot B.

6-5 Describing Distributions CAN YOU describe the shape of data distributions of a dot plot? CAN YOU describe the shape of data distributions of a box-and- whisker plot? CAN YOU make conclusions about data displayed on two box-and-whisker plots?

6-5 Describing Distributions HOMEWORK