Question

2 dot plots. Both number lines go from 0 to 10. Plot 1 is titled fifth grade. There are 2 dots above 1, 3 above 2, 1 above 3, 4 above 4, 5 above 5, 5 above 6, 2 above 7, 2 above 8, 0 above 9, 0 above 10. Plot 2 is titled seventh grade. There are 2 dots above 0, 2 above 1, 3 above 2, 5 above 3, 5 above 4, 3 above 5, 3 above 6, 1 above 7, and 0 above 8, 9, and 10.

The dot plot shows the number of hours, to the nearest hour, that a sample of 5th- and 7th-grade students spend watching television each week. How do the medians compare?

The 5th-grade range is
.

The 7th-grade range is
.

The ratio of variation of 5th grade to 7th grade is
.

Answer 1

The median amount of time that fifth-grade students spend watching television is 5 hours, whereas for seventh-grade students it is 4 hours. Both fifth and seventh graders have the same range of 7 hours in the number of hours spent watching television. The ratio of their ranges is 1:1.

Step-by-step explanation:

The question involves comparing the medians and ranges of hours spent watching television per week by 5th-grade and 7th-grade students using dot plots. To find the median, we list the number of hours in order for each grade and find the middle value(s). In the fifth-grade dot plot, there are 24 data points, so the median will be the average of the 12th and 13th points which both fall at 5 hours. For the seventh-grade dot plot, there are also 24 data points, and the median is the average of the 12th and 13th points which fall at 4 hours. Thus, the median for the fifth-grade is 5 hours, and for the seventh grade, it is 4 hours.

To find the ranges, we look at the smallest and largest values in the dot plots. The fifth-grade range is from 1 to 8 (8 - 1 = 7 hours), and the seventh-grade range is from 0 to 7 (7 - 0 = 7 hours), both are 7 hours wide. The ratio of variation, which can be interpreted as the range, between fifth grade and seventh grade is 1:1 since both have a range of 7 hours.