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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Byju's Answer

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.

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

3.5

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3.25

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Solution

The correct option is A 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.

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

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

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

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Q. Match the following:

\begin{matrix} Column A & Column B 1. A = {x : x i s a n o d d n a t u r a l n u m b e r} & a . {\frac{1}{2}, \frac{1}{3}, \frac{2}{3}, \frac{3}{4}, \frac{3}{5}, \frac{5}{7}} 2. B = {x : x = (n^{2}), n \in N a n d x < 100} & b . {1, 4, 9, 16, 25, . . . . . . . .10000} 3. C = {x : x = \frac{n}{n + 2}, n \in N a n d 1 \leq n \leq 6} & c . {1, 4, 9, 16, 25, 36, 49, 64, 81} 4. D = {x : x i s a l e t t e r o f t h e w o r d T R I G O N O M E T R Y} & d . {G, E, I, M, N, O, R, T, Y} e . {1, 3, 5, 7, 9, . . . . . . . . . . . . . . .} \end{matrix}

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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.

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