Question

based on the two data sets represented below, complete the following sentences. data set s data set t answer the mean of data set s is than the mean of data set t. the range of data set s is than the range of data set t.

Explanation:

Step1: Recall mean formula

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $x_{i}$ are data - points and $n$ is the number of data - points.

Step2: Estimate mean of Data Set S

Data Set S has most data - points concentrated around 72 - 78. The values seem to be relatively larger on average.

Step3: Estimate mean of Data Set T

Data Set T has data - points more spread out towards the lower values (68 - 74). So, its mean is likely to be smaller. Thus, the mean of Data Set S is greater than the mean of Data Set T.

Step4: Recall range formula

The range $R = \text{max}-\text{min}$.

Step5: Find range of Data Set S

In Data Set S, $\text{min}=71$, $\text{max}=78$, so $R_S=78 - 71=7$.

Step6: Find range of Data Set T

In Data Set T, $\text{min}=68$, $\text{max}=74$, so $R_T=74 - 68 = 6$. So, the range of Data Set S is greater than the range of Data Set T.

Answer:

The mean of Data Set S is greater than the mean of Data Set T. The range of Data Set S is greater than the range of Data Set T.