A driver records the distance travelled in each of 150 journeys. These distances, correct to the nearest $$\(\mathrm{km}\)$$, are summarised in the following table. Calculate an estimate of the mean distance travelled for the 150 journeys. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_m21_qp_52 Year：2021 Question No：5(c)
Answer:
Midpoints: \(2.25,7.5,15.5,25.5,35.5,50.5\)
\(\begin{array}{l}
\text { Mean }=\frac{2.25 \times 12+7.5 \times 16+15.5 \times 32+25.5 \times 66+35.5 \times 20+50.5 \times 4}{150}
=\frac{27+120+496+1683+710+202}{150}
{\left[=\frac{3238}{150}\right]=21.6,21 \frac{44}{75}}
\end{array}\)
\(\begin{array}{l}
\text { Mean }=\frac{2.25 \times 12+7.5 \times 16+15.5 \times 32+25.5 \times 66+35.5 \times 20+50.5 \times 4}{150}
=\frac{27+120+496+1683+710+202}{150}
{\left[=\frac{3238}{150}\right]=21.6,21 \frac{44}{75}}
\end{array}\)
Knowledge points:
5.1.5 calculate and use the mean and standard deviation of a set of data (including grouped data) either from the data itself or from given totals , and use such totals in solving problems which may involve up to two data sets.
Solution:
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