Question

The following is the distribution of height of students of a certain class in a certain city. Find the median height. Height ( in cm) 120-130 130-140 140-150 150-160 160-170 Total
No. of students 2 8 12 20 8 50

Answer 1

Step-by-step explanation:

Given that:

The following is the distribution of height of students of a certain class in a certain city. Find the median height. Height ( in cm) 120-130 130-140 140-150 150-160 160-170 Total

No. of students 2 8 12 20 8 50

To find:Compute the median height

Solution: To find the median height, first we have to find cumulative frequency.

For that tabulate the given data

$\begin{tabular}{|c|c|c|c|}\cline{1-3}Height(in\:cm.)& Number\:of\: students(f_i)& Cumulative\:frequency(CF)\\\cline{1-3}120-130&2&2\\\cline{1-3}130-140&8&10\\\cline{1-3}140-150&12&22\\\cline{1-3}\bold{150-160}&20&42\\\cline{1-3}160-170&8&50\\\cline{1-3}Total& 50&\\\cline{1-3}\end{tabular}$

$\boxed{Median:= l + \bigg( \frac{ \frac{n}{2} - cf}{f}\bigg) \times h}$

here

l= Lower limit of Median class

n/2=Total frequency divided by 2

cf: Cumulative frequency of preceding class

F: frequency of Median class

h= height of Median class

To find median class:

$\frac{n}{2} = \frac{50}{2} = 25$

search a class which has nearest to 25 in CF but not less than 25.

150-160 : Median class

l= 150

n/2=25

cf=22

f=20

h= 10

put these values to formula of median

$Median= 150+ \bigg(\frac{ 25- 22}{20} \bigg) \times 10 \\ \\ Median = 150 + \frac{30}{20} \\ \\ = 150+ 1.5 \\ \\Median = 151.5\:cm$

Median height of families is 151.5 cm

Hope it helps you.

Answer 2

Answer:

Median height of families is 151.5 cm.