Mathematics · Statistics · NCERT Examples

Example 7

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Mathematics · Chapter 13 · NCERT Examples

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NCERT Example

Example 7

median · less-than cumulative frequency · heights

The following less-than cumulative-frequency distribution gives the heights of 51 Class X girls. Find the median height.

Height (cm)

Girls

Less than 140

4

Less than 145

11

Less than 150

29

Less than 155

40

Less than 160

46

Less than 165

51

Solution

Board-exam working:

Subtract successive cumulative frequencies to obtain class frequencies.

Class

Frequency

Cumulative frequency

Below 140

4

4

140–145

7

11

145–150

18

29

150–155

11

40

155–160

6

46

160–165

5

51

n=51,n2=25.5n=51,\qquad \frac n2=25.5

The first cumulative frequency greater than 25.5 is 29, so the median class is 145–150.

l=145,cf=11,f=18,h=5l=145,\quad cf=11,\quad f=18,\quad h=5
Median=l+n2−cff×h\text{Median}=l+\frac{\frac n2-cf}{f}\times h
=145+25.5−1118×5=145+\frac{25.5-11}{18}\times5
=145+72.518=149.027…=145+\frac{72.5}{18}=149.027\ldots

Final answer

Median height≈149.03 cm\boxed{\text{Median height}\approx149.03\text{ cm}}

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