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Mathematics · Statistics · NCERT Examples

Example 5

A complete, independently verified solution for NCERT Example 5.

Mathematics · Chapter 13 · NCERT Examples

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NCERT Example

Example 5

mode · grouped data · modal class

A survey of 20 households gave the following frequency table for family size. Find the mode.

Family size

Families

1–3

7

3–5

8

5–7

2

7–9

2

9–11

1

Solution

Board-exam working:

The highest frequency is 8, so the modal class is 3–5.

l=3,h=2,f1=8,f0=7,f2=2l=3,\quad h=2,\quad f_1=8,\quad f_0=7,\quad f_2=2
Mode=l+f1−f02f1−f0−f2×h\text{Mode}=l+\frac{f_1-f_0}{2f_1-f_0-f_2}\times h
=3+8−72(8)−7−2×2=3+\frac{8-7}{2(8)-7-2}\times2
=3+27=3.2857…=3+\frac{2}{7}=3.2857\ldots

Final answer

Mode≈3.286 members\boxed{\text{Mode}\approx3.286\text{ members}}