A group of students were asked how long they spend practising mathematics during the week. The results are shown in the following table.

It is known that $35 < a < 52$ .

Write down

i)      the modal class;

ii)     the mid-interval value of the modal class;

iii)    the class in which the median lies.

For this group of students, the estimated mean number of hours spent practising mathematics is $2.69$.

Calculate the value of $a$ .

i)      $3 \leqslant t < 4$        (A1)    (C1)

Note: Accept equivalent notation: $[3,\,\,4)$ or $[3,\,\,4[$.

ii)     $3.5$        (A1)(ft)    (C1)

Note: Follow through from part (a)(i).

iii)    $2 \leqslant t < 3$        (A1)(ft)    (C1)

Note: Follow through from part (a)(i), for consistent misuse of inequality. Accept equivalent notation: $[2,\,\,3)$ or $[2,\,\,3[$.

$\frac{{3.5 \times 0.5 + 30 \times 1.5 + a \times 2.5 + 52 \times 3.5 + 43 \times 4.5}}{{35 + 30 + a + 52 + 43}} = 2.69$        (M1)(A1)(ft)

Notes: Award (M1) for substitution into mean formula and equating to $2.69$, (A1)(ft) for correct substitutions. Follow through from their mid-interval value in part (a)(ii).

$(a = )\,\,40$       (A1)(ft)     (C3)

Note: The final (A1)(ft) is awarded only if $a$ is an integer and $35 < a < 52$. Follow through from part (a)(ii).

Question 14: Grouped frequency table.

Candidates were able to identify the modal class and the class in which the median lies but few were able to find a missing value from the grouped frequency table given the estimated mean.

Question 14: Grouped frequency table.

Candidates were able to identify the modal class and the class in which the median lies but few were able to find a missing value from the grouped frequency table given the estimated mean.