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

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Solution

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

$Now, x_{k} = 85, h = 10, f_{k} = 32, f_{k - 1} = 30 and f_{k + 1} = 6 ∴ Mode, M_{0} = x_{k} + \{h \times \frac{(f_{k} - f_{k - 1})}{(2 f_{k} - f_{k - 1} - f_{k + 1})}\} = 85 + \{10 \times \frac{(32 - 30)}{(2 \times 32 - 30 - 6)}\} = 85 + \{10 \times \frac{2}{28}\} = (85 + . 71) = 85.71$

Hence, mode=85.71

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Similar questions

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

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

The following table gives the literacy rate (in percentage) in 40 cities. Find the mean literacy rate, choosing a suitable method.

Literacy rate (%)	45−55	55−65	65−75	75−85	85−95
Number of cities	4	11	12	9	4

Find the mean of the following using step deviation method.

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

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

As the class 85-95 has the maximum frequency, it is the modal class. Now, xk=85, h=10, fk=32, fk-1=30 and fk+1=6∴ Mode, M0=xk+h×fk-fk-12fk-fk-1-fk+1=85+10×32-302×32-30-6=85+10×228=85+.71=85.71 Hence, mode=85.71

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