MCQ
In a frequency distribution, the mid-value of a class is $15$ and the class intervals is $4$. The lower limit of the class is:
- A$10$
- B$12$
- ✓$13$
- D$14$
✓
Answer
Correct option: C.
$13$
Let $l$ and $m$ respectively be the lower and upper limits of the class. Then the mid-value of the class is $\frac{\text{l+m}}{2}$ and the class-size is $(m - l)$.
Therefore, we have two equations
$\frac{\text{l+m}}{2}=15$
$\Rightarrow l + m = 30,$
$m - l = 4$
Subtracting the second equation from the first equation, we have
$(l + m) - (m - l) = 30 - 4$
$\Rightarrow l + m - m + l = 26$
$\Rightarrow 2l = 26$
$\Rightarrow l = 13$
Hence, the lower limit of the class is $13$. Thus, the correct choice is $(c)$.
Therefore, we have two equations
$\frac{\text{l+m}}{2}=15$
$\Rightarrow l + m = 30,$
$m - l = 4$
Subtracting the second equation from the first equation, we have
$(l + m) - (m - l) = 30 - 4$
$\Rightarrow l + m - m + l = 26$
$\Rightarrow 2l = 26$
$\Rightarrow l = 13$
Hence, the lower limit of the class is $13$. Thus, the correct choice is $(c)$.
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