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The following data gives the information on the observed lifetimes (in hours) of $225$ electrical components:

What is the modal lifetime of the components?

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69.268

hours

65.625

hours

62.126

hours

58.267

hours

answer is B.

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Detailed Solution

It is given the information on the observed lifetimes (in hours) of

225

electrical components.
Question Image

We know that, mode of data is given as

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

From the data, we get that
Modal class of the given data is

60 - 80

.
Here,

l = 60, f_{0} = 52, f_{1} = 61, f_{2} = 38

and

h = 20

Putting these values in the formula, we get

Mode = 60 + {\frac{61 - 52}{122 - 52 - 38}} \times 20

\Rightarrow

Mode = 60 + \frac{9 \times 20}{32}

\Rightarrow Mode = 60 + \frac{45}{8}

\Rightarrow Mode = 60 + 5.625

\Rightarrow Mode

= 65.625

hours
Thus, the modal lifetime of the bulb is 65.625 hours.
Hence, the correct option is 2.

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The following data gives the information on the observed lifetimes (in hours) of 225electrical components:What is the modal lifetime of the components?

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The following data gives the information on the observed lifetimes (in hours) of $225$ electrical components:

What is the modal lifetime of the components?