The following data shows monthly savings of 100 families . Find the difference of modal and mean monthly savings in rupees.

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

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 D
800 - 900

Modal class is 4000-5000 with

$f_{1}$ = 27, $f_{0}$ = 21, $f_{2}$ = 25, I = 4000, h = 1000

Mode $= l + (\frac{f_{1} - f_{0}}{{2 f}_{1} - f_{0} - f_{2}}) \times h$

Mode $= 4000 + \frac{6}{8} \times 1000$

= 4750

Mean = $\frac{Σ f x}{Σ f}$

Mean = 3910

Difference between mode and mean = 4750 – 3910 = Rs. 840.

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The following data shows monthly savings of 100 families . Find the difference of modal and mean monthly savings in rupees. Monthly savings(Rs) Number of families 1000−2000142000−3000153000−4000214000−5000275000−600025

The correct option is D 800 - 900 Modal class is 4000-5000 with f1 = 27, f0 = 21, f2 = 25, I = 4000, h = 1000 Mode =l+(f1−f02f1−f0−f2)×h Mode =4000+68×1000 = 4750 Mean = ΣfxΣf Mean = 3910 Difference between mode and mean = 4750 – 3910 = Rs. 840.