Question

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:

High Low Q1 Q3 IQR Median Mean σ
College 20 6 8 18 10 14 13.3 5.2
High School 20 3 5.5 16 10.5 11 11 5.4

Which of the choices below best describes how to measure the spread of this data?
A. Both spreads are best described with the IQR.
B. Both spreads are best described with the standard deviation.
C. The college spread is best described by the IQR. The high school spread is best described by the standard deviation.
D. The college spread is best described by the standard deviation. The high school spread is best described by the IQR.

Answer 1

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

Explanation:

If data is normally distributed we use Standard deviation otherwise we use Interquartile Range (IQR) for measuring the spread.

Further, data is said to be normally distributed if Mean = Median = Mode.

So, High School data is normally distributed but College data is not.

So, We measure the spread of College data by IQR and High School data by Standard Deviation.

Thus, Option C is the only correct option.