The following data shows monthly savings of 100 families, the difference between modal and mean monthly savings lies between ___. (Given that modal class is the class having the highest frequency)

$\begin{matrix} M o n t h l y s a v i n g s (R s) & N u m b e r o f f a m i l i e s 1000 - 2000 & 14 2000 - 3000 & 15 3000 - 4000 & 21 4000 - 5000 & 27 5000 - 6000 & 25 \end{matrix}$

700-800

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600-700

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900-1000

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800 - 900

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Solution

The correct option is C
900-1000

Modal class is 4000-5000
$l = 4000; D_{1} = 27 - 21 = 6$
$D_{2} = 27 - 25 = 2; h = 1000$

$M o d e = l + (\frac{D_{1}}{D_{1} + D_{2}}) \times h 4000 + \frac{6}{8} \times 1000 = 750$

$M e a n = \frac{\sum F X}{\sum F} = \frac{391000}{100} = 3910$

Difference between mode and mean
= 4750 – 3910 = 840

840 lies between 800 and 900.

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The correct option is C 900-1000 Modal class is 4000-5000 l=4000; D1=27−21=6 D2=27−25=2;h=1000 Mode=l+(D1D1+D2)×h4000+68×1000=750 Mean=∑FX∑F=391000100=3910 Difference between mode and mean = 4750 – 3910 = 840 840 lies between 800 and 900.