6 5 Describing Distributions Learn describe and compare

6 -5 Describing Distributions Learn describe and compare data distributions by their center, spread, and shape, using box-and-whisker plots or dot 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. Shapes of a Distribution Skewed Normal Data are not symmetric about the center. Data are symmetric about the center. The measures of center may not be equal. The measures of center are equal.

6 -5 Describing Distributions Additional 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. 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 skewed. The mean, median, and mode are varied.

6 -5 Describing Distributions Check It Out: 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 skewed. The mean, median, and mode are varied.

6 -5 Describing Distributions Additional Example 2: Displaying Distributions on Box-and-Whisker Plots A. 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 data is skewed. The mean, median, and mode are varied.

6 -5 Describing Distributions Check It Out: Example 2 The data set and box-and-whisker plot display the number of pets that several students in Ms. Snow’s class own. Describe the shape of the data distribution. 9, 0, 4, 1, 1, 2, 3, 5, 2 The data is skewed. The mean, median, and mode are varied.

6 -5 Describing Distributions Additional 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 Check It Out: 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.