Dean Chalmers and Julian Gilbey Solutions for Chapter: Measures of Central Tendency, Exercise 9: END-OF-CHAPTER REVIEW EXERCISE 2

As part of a data collection exercise, members of a certain school year group were asked how long they spent on their Mathematics homework during one particular week. The times are given to the nearest $0.1$ hour. The results are displayed in the following table.

Calculate an estimate of the mean time spent on their Mathematics homework by members of this year group.

For $150$ values of $x,$ it is given that $\Sigma \left(x-1\right)+\Sigma \left(x-4\right)=4170.$ Find $\overline{x}.$

On Monday, a teacher asked eight students to write down a number, which is denoted by $x.$ On Tuesday, when one of these students was absent, they asked them to add $1$ to yesterday's number and write it down. Find the number written down on Monday by the student who was absent on Tuesday, given that $\overline{x}=30\frac{1}{4},$ and that the mean of Monday's and Tuesday's numbers combined was $27\frac{1}{3}.$

A delivery of $150$ boxes, each containing $20$ items, is made to a retailer. The numbers of damaged items in the boxes are shown in the following table.

Find the mode, the mean and the median number of damaged items.

A delivery of $150$ boxes, each containing $20$ items, is made to a retailer. The numbers of damaged items in the boxes are shown in the following table.

Which of the three measures of central tendency would be the most appropriate to use as the average in this case? Explain why using the other two measures could be misleading.

The monthly salaries, $w$ dollars, of $10$ women are such that $\Sigma \left(w-3000\right)=-200.$

The monthly salaries, $m$ dollars, of $20$ men are such that $\Sigma \left(m-4000\right)=120.$

Find the difference between the mean monthly salary of the women and the mean monthly salary of the men.

The monthly salaries, $w$ dollars, of $10$ women are such that $\Sigma \left(w-3000\right)=-200.$

The monthly salaries, $m$ dollars, of $20$ men are such that $\Sigma \left(m-4000\right)=120.$

Find the mean monthly salary of all the women and men together.

For $90$ values of $x$ and $64$ values of $y,$ it is given that $\Sigma \left(x-1\right)=72.9$ and $\Sigma \left(y+1\right)=201.6.$ Find the mean value of all the values of $x$ and $y$ combined.