Question

The following refer to the following data set:92.7 107.5 105.4 134.3 134.3116.8 127.8 134.3 110.3 117.2What is the arithmetic mean of this data set?mean =What is the median of this data set?median =What is the mode of this data set?mode

Answer 1

mean = 118.06

median = 117

mode = 134.3

Explanation

The mean is computed as follows:

`mean=\frac{sum\text{ of the observations}}{total\text{ number of observations}}`

In this case:

`\begin{gathered} \text{ mean }=(92.7+107.5+105.4+134.3+134.3+116.8+127.8+134.3+110.3+117.2)/(10) \\ \text{mean}=(1180.6)/(10) \\ \text{mean}=118.06 \end{gathered}`

To find the mode, first, we need to order the values from least to greatest, as follows:

92.7, 105.4, 107.5, 110.3, 116.8, 117.2, 127.8, 134.3, 134.3, 134.3

The median is the number of this ordered list. Given that there are 10 values, then there are 2 middle numbers, one at the 5th position, and another at the 6th position. In these cases, the median is the average between these two numbers, that is,

`\begin{gathered} \text{ median}=(116.8+117.2)/(2) \\ \text{med}\imaginaryI\text{an}=(234)/(2) \\ \text{med}\imaginaryI\text{an}=117 \end{gathered}`

The mode is the most frequent value. In this case, the most frequent value is 134.3 with 3 appearances