The following data gives the information on the observed lifetimes (in hours) of 225 electrical components: Lifetimes \[ \text { in } \quad 20 \quad 40 \quad 60 \] hours) Frequency 10 \[ 35 \] 52 Determine the modal lifetimes of the components.

Maths · Measures of dispersion; calculation of mean, median, mode of grouped and ungrouped data

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

The following data gives the information on the observed lifetimes (in hours) of 225 electrical components: Lifetimes \( 0- \) \( \begin{array}{lll}\text { 20- } & \text { 40- } & \text { 60- }\end{array} \) \[ \text { in } \quad 20 \quad 40 \quad 60 \] hours) Frequency 10 \[ 35 \] 52 Determine the modal lifetimes of the components.

A. 69.268 hours
B. 65.625 hours
C. 62.126 hours
D. 58.267 hours

Step-by-step solution

The modal class is identified as the class with the highest frequency. Assuming cumulative frequencies: less than 20:10, less than 40:35, less than 60:52, and total 225, the class frequencies are 10, 25, 17, and 173 for 0-20, 20-40, 40-60, 60-80 respectively. The modal class is 60-80. Using the mode formula: Mode = l + ((f1 - f0) / (2f1 - f0 - f2)) * h = 60 + ((173 - 17) / (2*173 - 17 - 0)) * 20 = 60 + (156/329) * 20 = 60 + 3120/329 ≈ 69.268 hours.

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Step-by-step solution

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