We are given the following data of a survey from 10 students from two schools showing the number of hours spent doing homework last night.
Xavier Middle School: 0, 2, 2, 1, 1, 4, 3, 3, 4, 3
Yates Middle School: 1, 4, 6, 3, 3, 0, 2, 2, 6, 3
a. Which measure of center should the education board use to describe the data?
Mean, Median and Mode are the measures of central tendency.
When the distribution of data is symmetrical then mean is the preferred choice of central tendency whereas when the data is skewed then median is preferred.
When the data contains any outliers (odd values) then the median is preferred. (no outliers in the given case)
Mode is the preferred choice of central tendency when the data is of ordinal type (not applicable in this case)
Therefore, considering the above points, the education board should use "mean" to describe the data.
b. What can you infer using the measure of center?
Let us find the mean of both data sets
Recall that the mean is given by
![\operatorname{mean}=\frac{\text{sum of data points}}{\text{total number of data points}}]()
The mean of Xavier Middle School is
![\operatorname{mean}=(0+2+2+1+1+4+3+3+4+3)/(10)=(23)/(10)=2.3]()
The mean of Yates Middle School is
![\operatorname{mean}=(1+4+6+3+3+0+2+2+6+3)/(10)=(30)/(10)=3]()
Conclusion:
On average, a student from Xavier Middle School spent 2.3 hours doing homework last night.
On average, a student from Yates Middle School spent 3 hours doing homework last night.
On average, a student from Yates Middle School spent more time doing homework last night than a student from Xavier Middle School.