19M.2.SL.TZ1.T_1

pestleMathematicsAISLPaper 219M· sl-4-4-pearsons-scatter-diagrams-eqn-of-y-on-xsource ↗

A healthy human body temperature is 37.0 °C. Eight people were medically examined and the difference in their body temperature (°C), from 37.0 °C, was recorded. Their heartbeat (beats per minute) was also recorded.

Write down, for this set of data the mean temperature difference from 37 °C, $\bar x$ .

[1]

b.i.

Write down, for this set of data the mean number of heartbeats per minute, $\bar y$ .

[1]

b.ii.

Plot and label the point M( $\bar x$ , $\bar y$ ) on the scatter diagram.

[2]

Use your graphic display calculator to find the Pearson’s product–moment correlation coefficient, $r$ .

[2]

d.i.

Hence describe the correlation between temperature difference from 37 °C and heartbeat.

[2]

d.ii.

Draw the regression line $y$ on $x$ on the scatter diagram.

[2]

Markscheme / solution

0.025 $\left( {\frac{1}{{40}}} \right)$ (A1)

[1 mark]

b.i.

74 (A1)

[1 mark]

b.ii.

the point M labelled, correctly plotted on their diagram (A1)(A1)(ft)

Note: Award (A1) for labelled M. Do not accept any other label. Award (A1)(ft) for their point M correctly plotted. Follow through from part (b).

[2 marks]

0.807 (0.806797…) (G2)

[2 marks]

d.i.

(moderately) strong, positive (A1)(ft)(A1)(ft)

Note: Award (A1) for (moderately) strong, (A1) for positive. Follow through from part (d)(i). If there is no answer to part (d)(i), award at most (A0)(A1).

[2 marks]

d.ii.

their regression line correctly drawn on scatter diagram (A1)(ft)(A1)(ft)

Note: Award (A1)(ft) for a straight line, using a ruler, intercepting their mean point, and (A1)(ft) for intercepting the $y$ -axis at their 73.5 and the gradient of the line is positive. If graph paper is not used, award at most (A1)(A0). Follow through from part (e).

[2 marks]

Examiners’ report

[N/A]

b.i.

[N/A]

b.ii.

[N/A]

d.i.

[N/A]

d.ii.

[N/A]