The scatter diagram shows the number of hours of sunshine and the number of visitors, in hundreds, at a beach on each of twelve days. A line of best fit has...

Assessment: Mathematics 0580 | Paper 3 Mock 01 | Calculator (Core) Subject: Mathematics - 0580

Question 1 Report

The scatter diagram shows the number of hours of sunshine and the number of visitors, in hundreds, at a beach on each of twelve days. A line of best fit has been drawn.

(a) Write down the type of correlation shown. [1]

(b) Use the line of best fit to estimate the number of visitors, in hundreds, on a day with \(7\) hours of sunshine. [2]

(c) Give two reasons why the line of best fit should not be used to estimate the number of visitors on a day with \(15\) hours of sunshine. [2]

Answer Details

(a) The points rise from lower left to upper right: more hours of sunshine goes with more visitors. That is positive correlation [B1]. Correlation describes the direction of the trend, so the answer is a type, not a number.

(b) Use the line of best fit, not an individual plotted day. Find \(7\) on the hours axis, go vertically up to the line, then horizontally across to the visitors axis [M1]. The reading is

\[ 5.4 \text{ hundred visitors} \] [A1]

Any value from \(5.2\) to \(5.6\) is accepted, since a hand-drawn line and a reading between gridlines carry a small tolerance. The axis is already in hundreds, so the answer is left as \(5.4\) hundred rather than converted.

(c) Two separate reasons are needed:

  • \(15\) hours is outside the range of the data collected, so using the line there is extrapolation rather than reading within the evidence [B1].
  • The trend may not continue beyond the days that were recorded, for example the beach has a limited capacity, so the straight-line pattern cannot be assumed to hold [B1].

Saying "the line does not reach \(15\)" twice in different words scores once only. Give one reason about the data range and one about the trend not continuing.

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