Compute the mode from the following data- - Size amp-45-55 amp-55-65 amp-65-75 amp-75-85 amp-85-95 amp-95-105 amp-105-115- Frequency amp-7 amp-12 amp-17 amp-30 amp-32 amp-6 amp-10- -

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Standard X

Mathematics

Finding Mode for Grouped Data When Class Intervals Are Given

Compute the m...

Question

Compute the mode from the following data:
$\begin{matrix} Size & 45 - 55 & 55 - 65 & 65 - 75 & 75 - 85 & 85 - 95 & 95 - 105 & 105 - 115 Frequency & 7 & 12 & 17 & 30 & 32 & 6 & 10 \end{matrix}$

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Solution

As the class 85-95 has maximum frequency, so it is the modal class:

Therefore,
l=85, h=10, f=32 and f1=30 and f2=6

Mode = l+[h×(f−f1)/(2f−f1−f2)]

=85+[10×(32−30)/(2×64−30−6)]

= 85 + (5/7) = (85+0.71) = 85.71

Hence, mode = 85.71

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Similar questions

Q. Compute the mode from the following series:

Size	45-55	55-65	65-75	75-85	85-95	95-105	105-115
Frequency	7	12	17	30	32	6	10

Q. Calculate the mode for the following data

:

Weight	$45 - 55$	$55 - 65$	$65 - 75$	$75 - 85$	$85 - 95$
Number of persons	$1$	$2$	$3$	$10$	$7$

Find the mode of the following data.

$\begin{matrix} C l a s s i n t e r v a l & 25 - 35 & 35 - 45 & 45 - 55 & 55 - 65 & 65 - 75 & 75 - 85 & 85 - 95 F r e q u e n c y & 12 & 16 & 17 & 15 & 8 & 19 & 13 \end{matrix}$

Find the median of the following data: $\begin{matrix} Class interval & 25 - 35 & 35 - 45 & 45 - 55 & 55 - 65 & 65 - 75 & 75 - 85 & 85 - 95 Frequency & 12 & 16 & 17 & 15 & 8 & 19 & 13 \end{matrix}$

5 + 15 + 25 + 35 + 45 + 55 + 65 + 75 + 85 + 95 = ___

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Compute the mode from the following data: Size45−5555−6565−7575−8585−9595−105105−115Frequency712173032610

As the class 85-95 has maximum frequency, so it is the modal class: Therefore, l=85, h=10, f=32 and f1=30 and f2=6 Mode = l+[h×(f−f1)/(2f−f1−f2)] =85+[10×(32−30)/(2×64−30−6)] = 85 + (5/7) = (85+0.71) = 85.71 Hence, mode = 85.71

Compute the mode from the following data:
$\begin{matrix} Size & 45 - 55 & 55 - 65 & 65 - 75 & 75 - 85 & 85 - 95 & 95 - 105 & 105 - 115 Frequency & 7 & 12 & 17 & 30 & 32 & 6 & 10 \end{matrix}$

As the class 85-95 has maximum frequency, so it is the modal class:

Therefore,
l=85, h=10, f=32 and f1=30 and f2=6

Mode = l+[h×(f−f1)/(2f−f1−f2)]

=85+[10×(32−30)/(2×64−30−6)]

= 85 + (5/7) = (85+0.71) = 85.71

Hence, mode = 85.71