In a frequency distribution table, modal value of the wages of $130$ workers is Rs. $97.50$ . L $= 94.5$ , $f_{m} = x + 15; f_{1} = x; f_{2} = x + 5$ . Find the upper limit of the modal class.

96.5

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97.5

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98.5

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99.5

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Solution

The correct option is D $99.5$
We use the formula
$M o d e = L + \frac{f_{m} - f_{1}}{2 f_{m} - f_{1} - f_{2}} \times h$
$⟹ 97.50 = 94.5 + \frac{x + 15 - x}{2 (x + 15) - x - (x + 5)} \times h$
$⟹ 97.50 = 94.5 + \frac{15}{30 - 5} \times h$
$⟹ 97.50 = 94.5 + \frac{3}{5} \times h$
$⟹ 3 = \frac{3}{5} \times h$
$⟹ h = 5$
Upper limit $= Lower limit + h = 94.5 + 5 = 99.5$
Hence, option D is correct

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Similar questions

Q. Find the sum of lower limit of the modal class and upper limit of modal class from the following frequency distribution table for the given data:

Class	Frequency
$10 - 20$	$1$
$20 - 30$	$3$
$30 - 40$	$5$
$40 - 50$	$9$
$50 - 60$	$7$
$60 - 70$	$3$

The following is the formula for finding the mode of grouped data. State what p and q are.
Mode = $p + \frac{q - f_{0}}{(q - f_{0}) + (q - f_{2})} \times h$

Class	$65 - 85$	$85 - 105$	$105 - 125$	$125 - 145$	$145 - 165$	$165 - 185$	$185 - 205$
Frequency	$4$	$15$	$3$	$20$	$14$	$7$	$14$

Let us find the difference between upper class limit in median class and lower class limit of modal class of the frequency distribution table.

Q. Heights of students of class

X

are given in the following frequency distribution. Find the modal height.

In the formula for finding mode of a grouped data,

Mode = $X + (\frac{A - B}{2 A - B - C}) \times h$

$\begin{matrix} i) X & a) f r e q u e n c y o f t h e c l a s s p r e c e d i n g t h e m o d a l c l a s s i i) A & b) L o w e r l i m i t o f t h e m o d a l c l a s s i i i) B & c) frequency of the class succeeding the modal class i v) C & d) f r e q u e n c y o f t h e m o d a l c l a s s \end{matrix}$

Match the options.

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In a frequency distribution table, modal value of the wages of 130 workers is Rs. 97.50. L=94.5, fm=x+15;f1=x;f2=x+5. Find the upper limit of the modal class.

The correct option is D 99.5We use the formula Mode=L+fm−f12fm−f1−f2×h⟹97.50=94.5+x+15−x2(x+15)−x−(x+5)×h⟹97.50=94.5+1530−5×h⟹97.50=94.5+35×h⟹3=35×h⟹h=5Upper limit =Lower limit+h=94.5+5=99.5Hence, option D is correct

In a frequency distribution table, modal value of the wages of $130$ workers is Rs. $97.50$ . L $= 94.5$ , $f_{m} = x + 15; f_{1} = x; f_{2} = x + 5$ . Find the upper limit of the modal class.