A survey reading the heights (in cm) of 50 girls of a class was conducted and the following data was obtained:Height (in cm)120−130130−140140−150150−160160−170TotalNumber of girls281220850Find the mean, median and mode of the above data.

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Filo · Accepted Answer

Assume mean A=145Class interval =h=20Class                   Frequency fi​     Mid Point xi​    ui​=hxi​−A​                 fi​ui​             cf120−1302125−2−42130−1408135−1−810140−15012145=A0022150−1602015512042160−170816521650N=50∑fi​ui​=24Mean:xˉ=A+h(Nfi​ui​​)=145+10×24/50=149.8MedianN=50N/2=25cf just after 25 is 42So, I=150,h=10,f=20 and cf=cf of preceding class i.e. 22Median =I+⎩⎨⎧​h×f(2N​−cf)​⎭⎬⎫​=150+{10×(25−22)/20}=151.5Mode:We know, Mode =3 Median −2 Mean=3×151.5−2×149.5=159.9Mean =149.8, Median =1515.5 and Mode =154.9

Height (in $c m$ )	$120 - 130$	$130 - 140$	$140 - 150$	$150 - 160$	$160 - 170$	Total
Number of girls	$2$	$8$	$12$	$20$	$8$	$50$

Height (in $c m$ )	$120 - 130$	$130 - 140$	$140 - 150$	$150 - 160$	$160 - 170$	Total
Number of girls	$2$	$8$	$12$	$20$	$8$	$50$

Class	Frequency $f_{i}$	Mid Point $x_{i}$	$u_{i} = \frac{x _{i} - A}{h}$	$f_{i} u_{i}$	$c f$
$120 - 130$	$2$	$125$	$- 2$	$- 4$	$2$
$130 - 140$	$8$	$135$	$- 1$	$- 8$	$10$
$140 - 150$	$12$	$145 = A$	$0$	$0$	$22$
$150 - 160$	$20$	$155$	$1$	$20$	$42$
$160 - 170$	$8$	$165$	$2$	$16$	$50$
	$N = 50$		$\sum f_{i} u_{i} = 24$

Question Text	A survey reading the heights (in $c m$ ) of $50$ girls of a class was conducted and the following data was obtained: Find the mean, median and mode of the above data.
Answer Type	Text solution:1
Upvotes	150

A survey reading the heights (in $c m$ ) of $50$ girls of a class was conducted and the following data was obtained:

Height (in $c m$ ) $120 - 130$ $130 - 140$ $140 - 150$ $150 - 160$ $160 - 170$ Total
Number of girls $2$ $8$ $12$ $20$ $8$ $50$
Find the mean, median and mode of the above data.

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