Question

In a recent survey, students were asked how long they play video games in one sitting. The interquartile range of the length of play times was 43 minutes. Which of the following is the best interpretation of this value?

Fifty percent of the video game data is below 43 minutes.
The middle half of the video game data has a range that is 43 minutes wide.
The number of minutes played by students typically varies by about 43 minutes from the mean.
The difference between the smallest and largest values in the video game data was 43 minutes.

Answer 1

The middle half of the video game data has a range that is 43 minutes wide.

Explanation:

Answer 2

The middle half of the video game data has a range that is 43 minutes wide.

Explanation:

Given that:

Interquartile range = 43 minutes

The interquartile range is obtained by taking the difference of the third quartile (Q3) and first quartile (Q1) value (Q3 - Q1) Hence, the interquartile range contains the middle 50% of the sample and the obtained value gives the variability or spread of the middle 50% of sample data. (Q3 - Q1) gives the spread between the upper and lower bound of the data which corresponds to the middle 50 % of the data.

In the example above, the spread is 43 minutes and is therefore, the range of the middle half(50%) of the sample data.