Question

1.13 A manufacturer of electronic components is in terested 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 (a) Find the sample mean and median. (b) What feature in this data set is responsible for the substantial difference between the two?

Answer 1

a)

$Mean=\frac{sum \:of\:terms}{No.\:of\:terms}\\ =\frac{123 + 116 + 122 + 110 + 175 + 126 + 125 + 111 + 118 + 117}{10}\\ =\frac{1243}{10}\\ Mean \:will\:be\:the\:\\ mean = \boldsymbol{124.3}$

The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

110   111   116   117   118   122   123   125   126   175   

As you can see, we do not have just one middle number but we have a pair of middle numbers, so the median is the average of these two numbers:

$Median=\frac{188+122}{2}=\boldsymbol{120}$

b)

Due to the outlier 175 is the outlier