Question

The following table shows the marks obtained by 100 students of class X in a school during a particular academic session. Find the mode of this distribution.

Marks No. of students

Less than 10 7

Less than 20 21

Less than 30 34

Less than 40 46

Less than 50 66

Less than 60 77

Less than 70 92

Less than 80 100

Answer 1

The mode is 'less than 80'.

Answer 2

Answer:

44.70

Step-by-step explanation:

Marks              No. of students(c.f.)            Frequency

Less than 10               7                                  7

Less than 20             21                                 14

Less than 30             34                                13

Less than 40             46                                12

Less than 50             66                                20

Less than 60             77                                11

Less than 70             92                               15

Less than 80            100                              8

Since the modal class (40-50) has highest frequency

So, the modal class is  40-50

Formula of Mode : $l+\frac{f_1-f_0}{2f_1-f_0-f_2}h$

where l is the lower limit of class

$f_1$ is the frequency of the class

$f_0$ is the preceding frequency

$f_2$ is the succeeding frequency

h is the class height

So l = 40

$f_1=20$

$f_0=12$

$f_2=11$

h = 10

Substitute the values in the formula

$Mode=40+\frac{20-12}{2(20)-12-11}(10)$

$Mode=44.70$

Hence the mode of the given data is 44.70