Question

A random survey of seventh- and eighth-grade students was conducted to find out how many hours is spent doing homework each night. Which of the following conclusions may be made by comparing the interquartile ranges of each data set? Select all that apply.

Answer 1

The interquartile range of both sets is equal to 1 hour.

The data sets exhibit similar variability, or spread.

Explanation:

Here is the question (attachment).

Random survey of the seventh and eighth grades students.

• Interquartile range (IQR) :

The IQR is the range of the middle 50% of scores.

IQR = Upperquartile - Lowerquartile

IQR = Q3 -Q1

IQR of (seventh grader) =
`4-3 =1`

IQR of (eight grader) =
`4.5-3.5=1`

• Normal curve represents perfect symmetric distribution as median and mean lie on the same position so they are neither negatively skewed nor positively skewed.
• None of the data is skewed more or less.
• Regarding the spread it exhibits similar variability.
• In similar variability the range is same.
• Range is the difference between highest and lowest values.
• Range =
  `R_7(4.5-2.5)=2,\ R_8=(5-3)=2`

Conclusion:

The interquartile range of both sets is equal to 1 hour.

The data sets exhibit similar variability, or spread.