Question

The amount of money that college students spend on rent each month is usually between $300 and $600. However, there are a few students who spend $1,300. What measure of spread would be most appropriate to measure the amount of money that college students spend on rent per month?
A. median
B. range
C. standard deviation
D. interquartile range

Answer 1

Answer: D. interquartile range

Step-by-step explanation:

Range and interquartile range both measures of the spread of data.

When data has no outlier , then the range is the best to measure the spread of data.

When data has outlier , then the interquartile range is the best to measure the spread of data because range gets affected by outliers  .

Given : The amount of money that college students spend on rent each month is usually between $300 and $600. However, there are a few students who spend $1,300.

$1,300 is an extreme value (outlier) as compare to the given range.

Hence, the measure of spread would be most appropriate to measure the amount of money that college students spend on rent per month = " interquartile range"

Answer 2

The correct answer is:

A) median.

Explanation:

When measuring the spread of this data, the first thing we note is that $1300 is an outlier; it is much, much different from the rest of the data. Therefore it has the potential to skew some measures of spread. For instance, the mean (not in this list) would be affected, since 1300 will raise the mean higher than it should be.

Since 1300 affects the mean, it also affects the standard deviation, which is the average distance each point is from the mean. Therefore standard deviation is not the best measure to use.

The range will be affected by this value as well, since this is the highest value; without it, the highest would be much less, which would make the range much less. Therefore range is not the best measure.

The interquartile range is not affected much by an outlier, but it is not usually a measure of spread that we use to describe values such as this.

We typically use the median to describe these values; since it is in the middle, it is not really affected by any outliers, and it is not a range from lowest to highest, such as the interquartile range (lowest quartile to highest quartile). Therefore median is the best measure.