3. An experiment to study the lifetime (hr) for a certain type of component invo

Question

3. An experiment to study the lifetime (hr) for a certain type of component involved putting 10 components into operation and observing them for 100 hours. Eight of the components failed during that period, and those lifetimes were recorded. Denote the lifetimes of the two components still functioning after 100 hours by 100+ (these data have been censored from the right). The sample observations were: 48, 79, 100+. 35, 92, 85, 57, 17, 100+,29 (a) Which of the measures of center for empirical data can be determined for this experiment (mean, median, mode)? Explain, for each measure of center, why it can or cannot be used (b) Find the value for any measure of center you believe possible for these data.

Explanation / Answer

a) Mean cannot be used here because the values of lifetime of 2 components are still unknown.

Mode cannot be used because the data given is continous distribution and sample size is less. Mode is suitable for discrete or categorical data. So, we cannot use mode here.

Median can be used to determine the center of the data

b) Data in ascending order - 17, 29, 35, 48, 57, 79, 85, 92, 100+, 100+

Median = average of 5th and 6th observations

= (57+79)/2

= 68 hours

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