The line plot shows the number of hours two groups of teens spent studying last week. How does the data compare for the two groups of teens? The mode for the hours spent studying last week for the 13 - to 15-year olds is less than the mode for the hours spent studying last week for the 16 - to 18-year olds. The median value for the hours spent studying last week for the 13 - to 15-year olds is greater than the median value for the hours spent studying last week for the 16 - to 18-year olds. The 13 - to 15-year olds spent an average of 14 hours studying last week. The range for the hours spent studying last week for the 13 - to 15-year olds is the same as the range for the hours spent studying last week for the 16 - to 18-year olds.

Question

Zachariah

Mathematics

11 May, 20:20

The line plot shows the number of hours two groups of teens spent studying last week. How does the data compare for the two groups of teens? The mode for the hours spent studying last week for the 13 - to 15-year olds is less than the mode for the hours spent studying last week for the 16 - to 18-year olds. The median value for the hours spent studying last week for the 13 - to 15-year olds is greater than the median value for the hours spent studying last week for the 16 - to 18-year olds. The 13 - to 15-year olds spent an average of 14 hours studying last week. The range for the hours spent studying last week for the 13 - to 15-year olds is the same as the range for the hours spent studying last week for the 16 - to 18-year olds.

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Answers (1)

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Olivia · Answer 1

The answer is that the median value for the 13-15 year olds is greater than the median value for the 16-18 year olds.

What I do to test this is this:

E. g. 13-15 year olds:

I write down the number of hours studying each time it shows up, in increasing order, like this:

6 7 8 10 12 12 12 13 14 14

Start crossing out numbers on each side until you make your way to the median:

7 8 10 12 12 12 13 14

8 10 12 12 12 13

etc. etc.

you'll reach

12 12

You need to take the average of the 2 for the median, which is just 12.

Next, do the same for the 16-18 year olds.

3 8 9 9 9 10 13 14 15 18

Start crossing out numbers on each side until you reach a median.

8 9 9 9 10 13 14 15

9 9 9 10 13 14

etc.

You'll reach

9 10

Take the average for the median, which is 9.5.

Therefore the median for the 13-15 year olds is 12 hours, while the 16-18 year olds is 9.5 hours, proving that the median for the 13-15 year olds is greater.

To disprove the other answers:We know the range for each age group is different because the 13-15 year olds range is 6-14 hours while the 16-18 year olds range is 3-18 hours.

To find the average of the 13-15 year olds hours studying, add up all the hours (6,7,8,10,12,13,14) and divide them by the number of categories you added (7 categories of hours). The answer is not 14, it's 10.

The mode is whichever hour appears the most. For the 16-18 year olds, it's 9 hours, as there are 3 dots there, and for the 13-15 year olds, it's 12 hours as there are 3 dots there. Therefore the 13-15 year olds study hours are not less than the 16-18 year olds, and therefore this statement is false