Question

13. The following distribution shows the marks scored by 140 students in an examination. Calculate the mode of
the distribution:​

Answer 1

Answer:

mode class = f1 =40

l = 20

f0=24

f2 = 36

h = 10

Step-by-step explanation:

mode = l + (f1-f0/2f1-f0-f2)*h

20+(40-24/2(40) -24-36)*10

= 20+(16/20)*10

= 20+8

=28

so mode is 28

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Answer 2

Given:

Number of students = 140

Distribution of students in each class

To find:

Mode of distribution =?

Solution:

Mode is the data that occurs frequently from all the observations.

When data are distributed in different classes the class which has maximum data is called the modal class.

Modal class = class 20-30

Marks scored by students (modal class) = 40

Formula to calculate mode is:

Mode of distribution (Z) = l + $\frac{f1 -f0}{2f1-f0-f2}$ × h

l = lower limit = 20

h = length of class (modal) = 10

f1 = frequency of class with maximum frequency = 40

f0 = frequency of class before f1 = 24

f2 = frequency of class after f2 = 36

Z = 20 + $\frac{40-24}{2*40 - 24 -36}$ × 10

Z = 20 + $\frac{16}{80-60}$ × 10

Z = 20 + $\frac{16}{20}$ × 10

Z =20 + 8

Z = 28

Mode of distribution = 28

Hence, the mode of distribution is 28.