Shapes of Distributions

University:
High School
Course:
High School Mathematics
Academic year:

2022
Views:

370

Pages:

4
Author:

garrotar4i3

Shapes of Distributions In your own words, write the meaning of each vocabulary term. Histogram a bar graph display of data showing distribution "bins" of equal size frequency table will list the # of times a certain # comes up. Core Concepts Symmetric and Skewed Distributions Skewed left: The "tail" of the graph extends to the left. Most of the data are on the right. Symmetric: The data on the right of the distribution are approximately a mirror image of the data on the left of the distribution. Skewed right: The "tail" of the graph extends to the right. Most of the data are on the left. Choosing Appropriate Measures When a data distribution is symmetric, use the mean to describe the center and use the standard deviation to describe the variation. When a data distribution is skewed, use the median to describe the center and use the five-number summary to describe the variation. 11.3 Extra Practice The table shows the average annual snowfall (in inches) of 26 cities. a. Display the data in a histogram using six intervals beginning with 15-28. histogram with six intervals: 1528, 2942, 4356, 5770, 7184, 8598, showing the frequency of cities in each interval. b. Which measures of center and variation best represent the data? Explain. Since this data is skewed right, use median for center and 5-number summary for variation. c. A weather station lists the top 20 snowiest major cities. The city in 20th place had 51 inches of snow. How would you interpret the data? The 20 snowiest city is in the upper half of snowfall at 51 inches. The double histogram shows the distributions of monthly precipitation for two towns over a 50-month period. Compare the distributions using their shapes and appropriate measures of center and variation. double histogram showing monthly precipitation for two towns (City A and City B) City A has a precipitation of skew right City B has a precipitation that is (more) symmetric So for City A use median for the center and 5-# summary for variation. So for City B use mean for the center and standard deviation for variation.