98
A class teacher has the following absentees record of $30$ students of a class.
begin{tabular}{|c|c|c|c|c|c|c|}
hline Number of days & 0 - 4 & 4 - 8 & 8 - 12 & 12 - 16 & 16 - 20 & 20 - 24
hline Number of Absent students & 1 & 8 & x & 6 & 5 & y
hline
end{tabular}
If the mean number of days a student was absent is $12$, find the values of $x$ and $y$.
begin{tabular}{|c|c|c|c|c|c|c|}
hline Number of days & 0 - 4 & 4 - 8 & 8 - 12 & 12 - 16 & 16 - 20 & 20 - 24
hline Number of Absent students & 1 & 8 & x & 6 & 5 & y
hline
end{tabular}
If the mean number of days a student was absent is $12$, find the values of $x$ and $y$.
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begin{tabular}{|c|c|c|c|}
hline C.I. & $f_i$ & $x_i$ & $f_i x_i$
hline 0 - 4 & 1 & 2 & 2
hline 4 - 8 & 8 & 6 & 48
hline 8 - 12 & x & 10 & 10x
hline 12 - 16 & 6 & 14 & 84
hline 16 - 20 & 5 & 18 & 90
hline 20 - 24 & y & 22 & 22y
hline & $20 + x + y$ & & $224 + 10x + 22y$
hline
end{tabular}
Correct table: [2 marks]
$x + y + 20 = 30 \Rightarrow x + y = 10$ ---(i) [1 mark]
$12 = \frac{10x + 22y + 224}{30} \Rightarrow 5x + 11y = 68$ ---(ii) [1 mark]
Solving (i) and (ii) we get
$x = 7$ [1/2 mark]
$y = 3$ [1/2 mark]
hline C.I. & $f_i$ & $x_i$ & $f_i x_i$
hline 0 - 4 & 1 & 2 & 2
hline 4 - 8 & 8 & 6 & 48
hline 8 - 12 & x & 10 & 10x
hline 12 - 16 & 6 & 14 & 84
hline 16 - 20 & 5 & 18 & 90
hline 20 - 24 & y & 22 & 22y
hline & $20 + x + y$ & & $224 + 10x + 22y$
hline
end{tabular}
Correct table: [2 marks]
$x + y + 20 = 30 \Rightarrow x + y = 10$ ---(i) [1 mark]
$12 = \frac{10x + 22y + 224}{30} \Rightarrow 5x + 11y = 68$ ---(ii) [1 mark]
Solving (i) and (ii) we get
$x = 7$ [1/2 mark]
$y = 3$ [1/2 mark]