Question

the mark distribution of 30 students in a mathematics examination are given below. Find the mode of this data.

Answer 1

Here is your answer dear

Answer 2

Answer:

The mode of the given data calculated is $52$.

Step-by-step explanation:

Data given:

The student's total number = $30$

Class interval        Student's number

$10-25$                              $2$

$25-40$                              $3$

$40-55$                              $7$

$55-70$                              $6$

$70-85$                              $6$

$85-100$                            $6$  

To find: The mode of the above data =?

As we know,

• Mode = $L + [\frac{f_{1} - f_{0} }{2f_{1} -f_{0}- f_{2} } ]\times h$

Here,

• L = Modal class's lower limit
• h = Class interval's size
• $f_{1}$ = Modal class's frequency
• $f_{0}$ = The class prior to the modal class's frequency
• $f_{2}$ = The class next to the modal class's frequency

Now, from the given data, we have to find out the above values:

Class interval        Student's number( $f_{i}$ )

$10-25$                              $2$

$25-40$                              $3$       -------$f_{0}$

$40-55$                              $7$       -------$f_{1}$   ( modal class )

$55-70$                              $6$       -------$f_{2}$

$70-85$                              $6$

$85-100$                            $6$

As we can see, the maximum number of students ( $7$ ) is in the class interval $40-50$.

Therefore, modal class is $40-50$.

Now,

• L = $40$
• h = $15$
• $f_{1}$ = $7$
• $f_{0}$ = $3$
• $f_{2}$ = $6$

Therefore,

• Mode = $L + [\frac{f_{1} - f_{0} }{2f_{1} -f_{0}- f_{2} } ]\times h$
• Mode = $40 + [\frac{7 - 3 }{2(7) -3- 6 } ]\times 15$
• Mode = $40 + [\frac{4 }{5 } ]\times 15$
• Mode = $40 +12$ = $52$

Hence, the mode of the above data is $52$.