Question

Miles  Freq
 0-4     3
 5-9    14
10-14   13
15-19    4

Write two sentences for non-statisticians expressing Chebyshev’s Theorem. Select the most appropriate sentence corresponding to two standard deviations.

*About 68% of students drive between 5.5212 miles and 13.7730 miles to somewhere
*At least 88.9% of students drive between -2.7306 miles and 22.0248 miles to 
*About 99.7% of students drive between 1.3953 miles and 17.8989 miles to 
*About 68% of students drive less than 22.0248 miles to
*About 95% of students drive between 5.5212 miles and 13.7730 miles to
*About 99.7% of students drive between -2.7306 miles and 22.0248 miles to
*About 68% of students drive between 1.3953 miles and 17.8989 miles to
*About 99.7% of students drive between 5.5212 miles and 13.7730 miles to
*At least 75% of students drive between -2.7306 miles and 22.0248 miles to
*At least 75% of students drive less than 22.0248 miles to
*About 95% of students drive between 1.3953 miles and 17.8989 miles to
*At least 75% of students drive between 1.3953 miles and 17.8989 miles to
*About 95% of students drive less than 22.0248 miles to 
*At least 88.9% of students drive between 1.3953 miles and 17.8989 miles to
*About 99.7% of students drive less than 22.0248 miles to
*About 95% of students drive between -2.7306 miles and 22.0248 miles to
*At least 88.9% of students drive less than 22.0248 miles to
*About 68% of students drive between -2.7306 miles and 22.0248 miles to

Answer 1

First we need to find the mean and SD of data:

Miles	X	Freq, f	xf	f(x-mean)^2
0-4	2	3	6	175.4344152
5-9	7	14	98	98.09993774
10-14	12	13	156	71.96979933
15-19	17	4	68	216.2605536
Total		34	328	561.7647059

Sample size:

The mean is:

The standard deviation is:

Interval corresponding to 2 standard deviations of mean is:

According to Chebyshev's theorem at least 75% data values lie within 2 standard deviations of mean. That is according to Chebyshev's theorem at least 75% data values lie within interval (1.3953, 17.7189).

-------------

Interval corresponding to 3 standard deviations of mean is:

According to Chebyshev's theorem at least 88.9% data values lie within 2 standard deviations of mean. That is according to Chebyshev's theorem at least 75% data values lie within interval (-2.7306, 22.0248).

Correct options are:

At least 75% of students drive between 1.3953 miles and 17.8989 miles

At least 88.9% of students drive between -2.7306 miles and 22.0248 miles