Question

Calculate Arithmetic Mean from the following data Marks : 4 8 12 16 20
No. of students : 6 12 18 15 9

Answer 1

Answer:

4 + 8 + 12 + 15 + 20 divided by 6 + 12 + 18 + 15 + 9

Answer 2

Given:

A data.

Marks: 4 8 12 16 20

No. of students: 6 12 18 15 9

To find:

Arithmetic Mean of the given data.

Solution:

The Arithmetic Mean of the given data is 12.6

To answer this question, we will follow the following steps:

As given, we have,

The number of students who got 4 marks = 6

So, the total marks = 4 × 6 = 24...(i)

Similarly,

The number of students who got 8 marks = 12

So, the total marks = 8 × 12 = 96...(ii)

The number of students who got 12 marks = 18

So, the total marks = 12 × 18 = 216...(iii)

The number of students who got 16 marks = 15

So, the total marks = 16 × 15 = 240...(iv)

The number of students who got 20 marks = 9

So, the total marks = 20 × 9 = 180...(v)

So,

The total marks of all students

$= 24 + 96 + 216 + 240 + 180$

$= 756$

[from (i), (ii), (iii), (iv) and (v)]

Also,

Total number of students

$= 6 + 12 + 18 + 15 + 9$

$= 60$

Hence,

The arithmetic mean

$= \frac{total \: marks \: of \: all \: students}{total \: number \: of \: students}$

$= \frac{756}{60}$

$= 12.6$

Hence, the Arithmetic Mean obtained from the given data is 12.6