97
The lengths of $40$ leaves of a plant are measured, correct to the nearest millimetre and data obtained is represented in the following table :
begin{tabular}{|c|c|}
hline Length in (mm) & Number of leaves
hline 100 - 120 & 8
hline 120 - 140 & 9
hline 140 - 160 & 12
hline 160 - 180 & 5
hline 180 - 200 & 6
hline
end{tabular}
Find the median length (in mm) of the leaves.
begin{tabular}{|c|c|}
hline Length in (mm) & Number of leaves
hline 100 - 120 & 8
hline 120 - 140 & 9
hline 140 - 160 & 12
hline 160 - 180 & 5
hline 180 - 200 & 6
hline
end{tabular}
Find the median length (in mm) of the leaves.
Show SolutionHide Solution↓
Solution: (a)
begin{tabular}{|c|c|c|}
hline C.I. & f & CF
hline 100 - 120 & 8 & 8
hline 120 - 140 & 9 & 17
hline 140 - 160 & 12 & 29
hline 160 - 180 & 5 & 34
hline 180 - 200 & 6 & 40
hline & 40 &
hline
end{tabular}
Correct table: [2 marks]
median class: $140 - 160$
$\text{Median} = l + \frac{\frac{N}{2} - cf}{f} \times h$
$= 140 + \frac{20 - 17}{12} \times 20$ [2 marks]
$= 145$ [1 mark]
$\therefore \text{The median length of the leaves is } 145$ mm
begin{tabular}{|c|c|c|}
hline C.I. & f & CF
hline 100 - 120 & 8 & 8
hline 120 - 140 & 9 & 17
hline 140 - 160 & 12 & 29
hline 160 - 180 & 5 & 34
hline 180 - 200 & 6 & 40
hline & 40 &
hline
end{tabular}
Correct table: [2 marks]
median class: $140 - 160$
$\text{Median} = l + \frac{\frac{N}{2} - cf}{f} \times h$
$= 140 + \frac{20 - 17}{12} \times 20$ [2 marks]
$= 145$ [1 mark]
$\therefore \text{The median length of the leaves is } 145$ mm