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Mathematics · Statistics · NCERT Examples

Example 6

A complete, independently verified solution for NCERT Example 6.

Mathematics · Chapter 13 · NCERT Examples

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NCERT Example

Example 6

mode · mean comparison · grouped marks

For the grouped marks distribution below, find the mode and compare it with the mean.

Marks

Students

10–25

2

25–40

3

40–55

7

55–70

6

70–85

6

85–100

6

Solution

Board-exam working:

The maximum frequency is 7, so the modal class is 40–55.

l=40,h=15,f1=7,f0=3,f2=6l=40,\quad h=15,\quad f_1=7,\quad f_0=3,\quad f_2=6
Mode=40+7−32(7)−3−6×15\text{Mode}=40+\frac{7-3}{2(7)-3-6}\times15
=40+45×15=52=40+\frac45\times15=52

The mean of the same grouped data is 62. The greatest concentration is around 52 marks, while the arithmetic average is 62 marks.

Final answer

Mode=52 marks;xˉ=62 marks\boxed{\text{Mode}=52\text{ marks};\quad \bar{x}=62\text{ marks}}