Question

Tim took a random survey of 20 sixth graders and 20 eighth graders. He asked how many hours a week each played sports. His data is shown in the two dot plots below + 0 1 2 3 4 5 6 7 8 9 10 6th Graders HHH 0 1 2 3 4 5 6 7 8 9 10 8th Graders.What is the difference between the median number of hours that sixth graders play sports and the median number of hours that 8th graders play sports?

Answer 1

From the dot plot, we have the following data:

For 6th grade:

Number of students Frequency(hours)

1 2

4 3

2 4

4 5

5 6

1 7

1 9

2 10

Now let's write down the number of hours, arranging them in ascending order:

2, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 6,6,6,6,6,7,9,10,10

To find the median of 6th grade, we sum up the two middle numbers, which are 5 and 5, and divide by 2.

Thus:

`\begin{gathered} m\text{edian of 6th grade = }(5+5)/(2) \\ =\text{ }(10)/(2) \\ =\text{ 5} \end{gathered}`

Median of hours that 6th grade play sports = 5 hours

Lets also use the same method to find the median for 8th grade.

For 8th grade:

Number of students Frequency(hours)

1 2

1 3

2 4

2 6

4 7

5 8

2 9

3 10

Now let's write down the number of hours, arranging them in ascending order:

2,3,4,4,6,6,7,7,7,7,8,8,8,8,8,9,9,10,10,10

To find the median of 8th grade, we sum up the two middle numbers, which are 7 and 7, and divide by 2.

Thus:

`\begin{gathered} m\text{edian of 8th grade = }(7+7)/(2) \\ =\text{ }(14)/(2) \\ =\text{ 7} \end{gathered}`

Median of hours that 8th graders play sports = 7 hours

The difference between the median number of hours that sixth graders play sports and the median number of hours that 8th graders play sports will be:

ANSWER:

2 HOURS