Here is a histogram of a distribution with 94 data points.
Histogram. The vertical axis is labeled from 0 to 12 by 2’s. The horizontal axis has bin widths of 1, starting at 46. Beginning at 46 up to, but not including 47, height of bar at each interval is 2, 3, 4, 3, 6, 8, 9, 12, 11, 8, 6, 8, 7, 4, 2, 1, 0.
For each given interval, find the proportion of data points that fall in that interval.
47 to 48
50 to 51
53 to 54
Problem 2
This relative frequency histogram shows the distribution of daily average temperatures (in degrees Fahrenheit) for a town over the course of 5 years.
Histogram from 60 to 78 by 1’s. Average daily temperature in degrees Fahrenheit. Beginning at 60 up to but not including 61, height of bar at each interval is point 0 0 1, point 0 0 7, point 0 1 3, point 0 2, point 0 5 2, point 0 7, point 0 8 7, point 1 2, point 1 5 9, point 1 3 2, point 1, point 0 9 8, point 0 7, point 0 3 2, point 0 2 3, point 0 1, point 0 0 4, point 0 0 2, 0.
Match each temperature interval with the proportion of days over the 5 years whose average temperature fell in that interval.
60 to 66 degrees Fahrenheit
66 to 68 degrees Fahrenheit
68 to 70 degrees Fahrenheit
70 to 71 degrees Fahrenheit
73 to 74 degrees Fahrenheit
0.032
0.10
0.163
0.207
0.291
Problem 3
Two curves representing normal distributions are shown. Does the solid curve or dashed curve have a greater standard deviation? Explain how you know.
A bell-shaped distribution. The bell is centered 6 units right and 7.5 units up. Another bell-shaped distribution, a dotted line on the same axis, is shorter and wider. It is centered at 6 units right, 5 units up.
Clare is designing an experimental study. She says that, in an experimental study, it is important to randomly assign people to groups because this helps reduce the likelihood of grouping subjects into groups that may differ on some characteristic that is related to the response of interest. Do you agree with Clare? Explain your reasoning.