Questions

The following data gives the information on the observed lifetimes (in hours) of 225

electrical components:

Lifetime (in hours) | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 | 100-120 |

Frequency | 10 | 35 | 52 | 61 | 38 | 29 |

Determine the modal lifetimes of the components.

detailed solution

Correct option is A

From the given data the modal class is 60–80.

l = 60,

The frequencies are:

f_{m} = 61, f_{1} = 52, f_{2} = 38 and h = 20

The formula to find the mode is

Mode *= l+ [*$\frac{{f}_{m}-{f}_{1}}{2{f}_{m}-{f}_{1}-{f}_{2}}$*]×h*

Substitute the values in the formula, we get

Mode =60+[$\frac{61-52}{122-52-38}$]×20

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

Mode = 60+($\frac{45}{8}$) = 60+ 5.625

Therefore, modal lifetime of the components = 65.625 hours.

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detailed solution

Correct answer is 1

From the given data the modal class is 60–80.

l = 60,

The frequencies are:

f_{m} = 61, f_{1} = 52, f_{2} = 38 and h = 20

The formula to find the mode is

Mode *= l+ [*$\frac{{f}_{m}-{f}_{1}}{2{f}_{m}-{f}_{1}-{f}_{2}}$*]×h*

Substitute the values in the formula, we get

Mode =60+[$\frac{61-52}{122-52-38}$]×20

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

Mode = 60+($\frac{45}{8}$) = 60+ 5.625

Therefore, modal lifetime of the components = 65.625 hours.

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