The following data shows the warranty period of different components- Find the modal warranty period- - Warranty periodyears 0 - 1 1 - 2 2 - 3 3 - 4 4 - 5 5 - 6- Number of components 6 10 16 25 16 20- -

Modal class is 3 4 since it is the class with highest frequency. Mode = l + [ f_1 f_0 /2 f_1 f_0 f_2] × nbsp;h f_1 represents the frequency of the mod ...

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Standard X

Mathematics

Finding Mode for Grouped Data Wen Class Intervals Are Not Given

The following...

Question

The following data shows the warranty period of different components. Find the modal warranty period.

$\begin{matrix} W a r r a n t y p e r i o d (y e a r s) & 0 - 1 & 1 - 2 & 2 - 3 & 3 - 4 & 4 - 5 & 5 - 6 N u m b e r o f c o m p o n e n t s & 6 & 10 & 16 & 25 & 16 & 20 \end{matrix}$

3.25

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3.5

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Solution

The correct option is C 3.5
Modal class is $3 - 4$ since it is the class with highest frequency.

$M o d e = l + [\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}}] \times h$
$f_{1}$ represents the frequency of the modal class.
Also,
$l =$ lower boundary of the modal class
$h =$ size of the modal class interval
$f_{0} =$ frequency of the class preceding the modal class
$f_{2} =$ frequency of the class succeeding the modal class

Here, $f_{1} = 25, f_{0} = 16, f_{2} = 16, l = 3, h = 1$

$\Rightarrow M o d e = 3 + [\frac{25 - 16}{2 \times 25 - 16 - 16}] \times 1 = 3.5$

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The following data shows the warranty period of different components. Find the modal warranty period. Warranty period(years)0−11−22−33−44−55−6Number of components61016251620

The following data shows the warranty period of different components. Find the modal warranty period.

$\begin{matrix} W a r r a n t y p e r i o d (y e a r s) & 0 - 1 & 1 - 2 & 2 - 3 & 3 - 4 & 4 - 5 & 5 - 6 N u m b e r o f c o m p o n e n t s & 6 & 10 & 16 & 25 & 16 & 20 \end{matrix}$