Mathematics 9709 · AS & A Level · Representation of data

Representation of data — practice question

The table gives a summary of the journey times to college for 2500 students. The variable is time taken $t$ minutes, with classes $0 \leq t < 20$, $20 \leq t < 30$, $30 \leq t < 40$, $40 \leq t < 60$, $60 \leq t < 90$ and the corresponding frequencies $440$, $720$, $920$, $300$, $120$.
(a)[4]

Construct a histogram to display this information.

(b)[3]

From the data, the estimated mean value of $t$ is $31.44$. Calculate an estimate of the standard deviation of the times taken to travel to college.

(c)[1]

In which class interval is the upper quartile found?

(d)[1]

It was later found that the times taken to travel to college for two students had been entered wrongly. One student’s time was written as $15$ instead of $5$ and the other’s time was written as $65$ instead of $75$. Without carrying out any further calculations, state with a reason whether the estimate of the standard deviation in part (b) would be increased, decreased or stay the same.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: At least four frequency densities correctly found

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