Question

find median and mode of the following distribution ​

Answer 1

Answer:

Hope this is OK for you completely

Answer 2

Step-by-step explanation:

Given:

Marks 0-10 10-20 20-30 30-40 40-50 50-60

Freq.__4___6____12___6____7___5

To find:Mode and Median

Solution:

1) Find Mode:

Formula used:

$\boxed{\bold{\red{Mode = l + \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \times h}}}$

here

l: lower limit of modal class

f0: Frequency preceding of modal class

f1: Frequency of modal class

f2: Frequency succeeding to modal class

h: height of modal class

Here,

Highest frequency is 12.

Thus,

Modal class:20-30

l=20

f0=6

f1=12

f2=6

h=10

put these values in formula

$Mode = l + \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \times h \\ \\ Mode = 20 + \left( \frac{12 - 6}{24 - 6 - 6} \right) \times 10 \\ \\ Mode = 20 + \frac{6}{12} \times 10 \\ \\ Mode = 20 + 5 \\ \\ \red{Mode = 25}$

2) Find median:

Formula used:

$\boxed{\bold{\green{Median = l + \left(\frac{ \frac{n}{2} - CF}{f} \right) \times h}}}$

here,

l: lower limit of Median class

n/2: Half of number of students

CF: Cumulative frequency of preceding to Median class

f: Frequency of Median class

h:height of median class

Class 0-10 10-20 20-30 30-40 40-50 50-60

F ___4___6____12___6____7_____5

CF__4___10___22___28___35____40

n/2= 20

Median class: 20-30

l=20

cf=10

f=12

h=10

put the values in the formula

$Median = 20+ \left(\frac{ 20 - 10}{12} \right) \times 10 \\ \\ Median = 20 + \frac{10}{12} \times 10 \\ \\ Median = 20 + \frac{25}{3} \\ \\ Median = 20 + 8.3 \\ \\ \green{Median = 28.3}$

Final answer:

Mode= 25

Median = 28.3

Hope it helps you.

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