A courier company records parcels delivered per driver. Over \(10\) drivers on route A the mean is \(34\) parcels. Over \(6\) drivers on route B the mean is...
Question 1 Report
A courier company records parcels delivered per driver. Over \(10\) drivers on route A the mean is \(34\) parcels. Over \(6\) drivers on route B the mean is \(m\) parcels. The combined mean over all \(16\) drivers on both routes is \(31\) parcels.
- Work out the value of \(m\). (3)
- State, with a reason, whether route B tends to have more or fewer parcels per driver than route A. (1)
Answer Details
Combining two group means correctly means converting each mean back into a total, adding the totals, and only then using the combined total and the given overall mean to find the missing group's total and its mean.
(a)
- Combined total \(=31\times16=496\), and route A's total \(=10\times34=340\) [1 mark]
- Route B's total \(=496-340=156\) [1 mark]
- \[ m=156\div6=26 \] [1 mark]
(b) Route B has fewer parcels per driver, since its mean of \(26\) is less than route A's mean of \(34\); this is why the combined mean of \(31\) is pulled below route A's mean of \(34\) rather than sitting exactly between the two routes' means. [1 mark]
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