Answer to Question #333181 in Statistics and Probability for Thabu

Question

A manufacturer of electronic components is interested in determining the lifetime of a certain type of battery. A sample, in hours of life, is as follows

123 116 122 110 175 126 125 111 118 117

(i) Determine the sample mean and median

(ii) What feature in this data set is responsible for the substantial difference between the two?

Answer 1

(i)

Sorted Data Set: 110, 111, 116, 117, 118, 122, 123, 125, 126, 175

$$mean=\dfrac{1}{10}(110+111+116+117$$

$$+118+122+123+125+126+175)=124.3$$

$$median=\dfrac{118+122}{2}=120$$

(ii)

The extreme value (175 hours) is responsible  for the substantial difference between the sample mean and sample median.