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Mean, Median, Mode of Grouped Data — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsMean, Median, Mode of Grouped Data5 Marks
Question
Calculate the missing frequency from the following distribution, it being given that the median of the distribution is 24.
Age (in years)
0-10
10-20
20-30
30-40
40-50
Number of persons
5
25
?
18
7
✓

Answer

Age (in years)
Number of persons (f)
Cumulative frequency (cf)
0-10
5
5
10-20
25
30
20-30
x
30 + x
30-40
18
48 + x
40-50
7
55 + x
Median = 24
Hence, median class is 20-30
$\therefore\text{l}=20,\ \text{h}=10,\ \text{f}=\text{a},\ \text{cf}=$ cf of preceding class $=30,\ \frac{\text{N}}{2}=\frac{55+\text{a}}{2}$
Now, median $=\text{l}+\begin{Bmatrix}\text{h}\times\frac{\Big(\frac{\text{N}}{2}-\text{cf}\Big)}{\text{f}}\end{Bmatrix}$
$\Rightarrow24=20+\begin{Bmatrix}10\times\frac{\Big(\frac{55+\text{a}}{2}-30\Big)}{2}\end{Bmatrix}$
$\Rightarrow4=10\times\frac{55+\text{a}-60}{2\text{a}}$
$\Rightarrow4=5\times\frac{\text{a}-5}{\text{a}}$
$\Rightarrow4\text{a}=5\text{a}-25$
$\Rightarrow\text{a}=25$
Thus, yhe missung frequency is 25.

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