Question

3. The following are the sizes in square feet of the seventeen new faculty office in the mathematics department at a college.102123142155104185159124154136113110107119120127155Find the mean square footage. Round your answer to the nearest tenth, if necessary. square feetFind the median square footage. square feet

Answer 1

Given a sample of the size, measured in square feet, of 17 faculty offices.

1) Mean

To calculate the mean of the sample you have to add all observations of the data set and divide it by the sample size:

`\bar{x}=(\Sigma x_i)/(n)`

The mean square footage is 131.5 ft²

2) Median

To determine the median of the data set, first, you have to calculate the position of the median, following the formula:

`\text{PosMe}=((n+1))/(2)`

The sample size is n=17, then the position of the median is

`\begin{gathered} \text{PosMe}=(17+1)/(2) \\ \text{PosMe}=(18)/(2) \\ \text{PosMe}=9 \end{gathered}`

The median corresponds to the ninth observation of the data set.

Next, you have to order the data set from least to greatest:

102, 104, 107, 110, 113, 119, 120, 123, 124, 127, 136, 142, 154, 155, 155, 159, 185

Count the ninth observation from the left.

The median of the data set is Me= 124 ft²