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Stastics — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsStastics1 Mark
MCQ
Look at the frequency distribution table given below:
Class interval
35-45
45-55
55-65
65-75
Frequency
8
12
20
10
The median of the above distribution is:
  • A
    56.5
  • ✓
    57.5
  • C
    58.5
  • D
    59
✓

Answer

Correct option: B.
57.5
b. 57.5
Solution:
Class intervalClass interval
FrequencyFrequency
Cumulative frequencyCumulative frequency
35-45
8
8
45-55
12
20
55-65
20
40
65-75
10
50
Here, $\text{N}=50\Rightarrow\frac{\text{N}}{2}=25$
The cumulaove frequency just greater than 25 is 40.
Hence, median class is 55-65.
Now, median $=\text{l}+\begin{Bmatrix}\text{h}\times\frac{\Big(\frac{\text{N}}{2}-\text{cf}\Big)}{\text{f}}\end{Bmatrix}$
$=55+\Big\{10\times\frac{(25-20)}{20}\Big\}$
$=55+2.5$
$=57.5$

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