Question

A class teacher has the following absentees record of $30$ students of a class.

| Number of days | $0 - 4$ | $4 - 8$ | $8 - 12$ | $12 - 16$ | $16 - 20$ | $20 - 24$ |
|---|---|---|---|---|---|---|
| Number of Absent students | $1$ | $8$ | $x$ | $6$ | $5$ | $y$ |

If the mean number of days a student was absent is $12$ , find the values of $x$ and $y$ .

Approach

Correct frequency table with midpoints. Total frequency $x + y + 20 = 30$ gives $x + y = 10$ . Mean $= \frac{Σ f _{i} x _{i}}{Σ f _{i}} = 12$ gives $10 x + 22 y + 224 = 360$ or $5 x + 11 y = 68$ . Solving, $x = 7$ and $y = 3$ .

Step-by-step working

1
Correct table with $x_{i}$ and $f_{i} x_{i}$
2 marks
2
$x + y + 20 = 30$ and $12 = \frac{10 x + 22 y + 224}{30}$
1 mark
3
Solving: $x + y = 10$ and $5 x + 11 y = 68$
1 mark
4
$x = 7$
0.5 marks
5
$y = 3$
0.5 marks

Concepts used

meangrouped datafrequency

Approach

Step-by-step working

Concepts used

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