Calculate the median of the farm size for the following data $:$
Farm size
$2 - 5$
$5 - 8$
$8 - 11$
$11 - 14$
$14 - 17$
Rooms
$4$
$8$
$12$
$16$
$20$

9.125

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8.125

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7.125

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6.125

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Solution

The correct option is B $9.125$
Farm size
Frequencies(f)
Cumulative frequency(cf)
$2-5
$4$
$4$
$5 - 8$
$8$
$4 + 8 = 12$
$8 - 11$
$12$
$12 + 12 = 24$
$11 - 14$
$16$
$24 + 16 = 40$
$14 - 17$
$20$
$40 + 20 = 60$

$n = Σ f = 60$
$\frac{n}{2} = \frac{60}{2} = 30$
Median $= l + ⎛ ⎜ ⎜ ⎝ \frac{\frac{n}{2} - c f}{f} ⎞ ⎟ ⎟ ⎠ \times h$
$n = Σ f =$ Total number of frequency $= 60$
$\frac{n}{2} = \frac{60}{2} = 30$
So, the median class is $11 - 14$
L $=$ Lower limit of the median class $= 11$
cf $=$ Cumulative frequency of the class preceding the median class $= 40$
f $=$ Frequency of the median class $= 16$
h $=$ class width $= 3$
Therefore, Median $= l + ⎛ ⎜ ⎜ ⎝ \frac{\frac{n}{2} - c f}{f} ⎞ ⎟ ⎟ ⎠ \times h$
$= 11 + ⎛ ⎜ ⎜ ⎜ ⎝ \frac{\frac{60}{2} - 40}{16} ⎞ ⎟ ⎟ ⎟ ⎠ \times 3$
$= 11 + (\frac{30 - 40}{16}) \times 3$
$= 11 - 1.875$
$= 9.125$
Hence, the median is $9.125$

Suggest Corrections

shoe size	$2$	$3$	$4$	$5$	$6$
frequency	$10$	$20$	$12$	$14$	$11$

Farm size	$12$	$13$	$14$	$15$	$17$	$18$	$19$	$20$
Number of animals	$3$	$4$	$4$	$2$	$1$	$2$	$4$	$1$

Farm size	$2 - 5$	$5 - 8$	$8 - 11$	$11 - 14$	$14 - 17$
Rooms	$4$	$8$	$12$	$16$	$20$

Size	$2 - 5$	$5 - 8$	$8 - 11$	$11 - 14$
Number of shoes	$1$	$4$	$8$	$7$