Question

question 2 (2 points)
the table below shows data from a survey about the amount of time students spend doing homework each week. the students were either in college
or in high school:
which of the choices below best describes how to measure the spread of this data?
( hint use the minimum and maximum values to check for outliers.) (2 points)
both spreads are best described with the iqr.
both spreads are best described with the standard deviation.
the college spread is best described by the iqr. the high school spread is best described by the standard deviation.
the college spread is best described by the standard deviation. the high school spread is best described by the iqr.

Explanation:

Step1: Recall the rules for choosing spread measure

If the data has outliers (checked using minimum and maximum values), the IQR (inter - quartile range) is a better measure of spread. If the data is symmetric (no outliers), the standard deviation is a better measure.

Step2: Analyze college data

For college data: Mean = 11.7, Median = 12. The mean and median are close, suggesting the data is relatively symmetric. So, standard deviation is a good measure of spread.

Step3: Analyze high - school data

For high - school data: Mean = 5.11, Median = 5. The mean and median are close. But we also check for outliers. Using the formula for outliers \(Q1 - 1.5\times IQR\) and \(Q3 + 1.5\times IQR\). \(IQR_{high - school}=Q3 - Q1=10.5 - 4.5 = 6\). \(Q1-1.5\times IQR=4.5-1.5\times6=-4.5\), \(Q3 + 1.5\times IQR=10.5+1.5\times6=19.5\). The minimum value \(3\gt - 4.5\) and maximum value \(28\gt19.5\). So, high - school data has an outlier (\(28\)). When there is an outlier, the IQR is a better measure of spread.

Answer:

d. The college spread is best described by the standard deviation. The high school spread is best described by the IQR.