Question

help!!!
The table 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?

Answer 1

question 4

Answer 2

Which of the choices below best describes how to measure the spread of this data?
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.

Answer 3

My only real concern is the magnitude of the Standard Deviation. How does this relate to the Mean versus the High and the Low in both cases?

Answer 4

im not sure @tkhunny

Answer 5

Calculate for both College and High School...

How many standard deviations from the Mean to the Minimum?
How many standard deviations from the Mean to the Maximum?

Then ask, according the the Empirical Rule, how many standard deviations should we expect to encompass a large percentage of a roughly normal-shaped distribution?

Answer 6

ive never done standard eviations

Answer 7

@tkhunny

Answer 8

thank you so much @amistre64

Answer 9

So? You can do it.

College
Mean: 13.3
Minimum: 6
Maximum: 20
Standard Deviation: 5.2

Standard Deviations to the Minimum: (13.3-6)/5.2 = 1.4
Standard Deviations to the Maximum: (20-13.3)/5.2 = 1.3

For a standard deviation to be truly representative, we should get around 3! Neither 1.3 nor 1.4 is very impressive. This suggests to me that the Standard Deviation very poorly describes the distribution.