carter is moving to gainesville, fl and wants to buy a house that is no more than 10 miles away from his new…

carter is moving to gainesville, fl and wants to buy a house that is no more than 10 miles away from his new job. the distances of the houses for sale from his new job, in miles, are shown below.\n0.2,0.5,0.9,1.2,1.5,1.6,2.2,2.7,2.9,3.1,4.8\ncomplete the statements.\nthe measure of the center that best describes the typical distance of the houses for sale from carters new job is \nthe measure of variation that best describes the spread of the data distribution is

carter is moving to gainesville, fl and wants to buy a house that is no more than 10 miles away from his new job. the distances of the houses for sale from his new job, in miles, are shown below.\n0.2,0.5,0.9,1.2,1.5,1.6,2.2,2.7,2.9,3.1,4.8\ncomplete the statements.\nthe measure of the center that best describes the typical distance of the houses for sale from carters new job is \nthe measure of variation that best describes the spread of the data distribution is

Answer

Explanation:

Step1: Analyze data set

The data set 0.2, 0.5, 0.9, 1.2, 1.5, 1.6, 2.2, 2.7, 2.9, 3.1, 4.8 is relatively small - sized and has no extreme outliers.

Step2: Choose measure of center

For a data - set without extreme outliers, the mean is a good measure of the center. The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $n = 11$ and $x_{i}$ are the data points. $\sum_{i=1}^{11}x_{i}=0.2 + 0.5+0.9+1.2+1.5+1.6+2.2+2.7+2.9+3.1+4.8 = 21.6$. So, $\bar{x}=\frac{21.6}{11}\approx1.96$.

Step3: Choose measure of variation

The standard deviation measures the average amount by which each data value differs from the mean. It is a good measure of variation for data sets with no extreme outliers. The formula for the sample standard deviation $s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}}$.

Answer:

The measure of the center that best describes the typical distance of the houses for sale from Carters new job is the mean. The measure of variation that best describes the spread of the data distribution is the standard deviation.