Question

mr. zuro finds the mean height of all 15 students in his statistics class to be 68.0 inches. just as mr. zuro finishes explaining how to get the mean, danielle walks in late. danielle is 71.2 inches tall. what is the mean height of the 16 students in the class? the mean height of the 16 students in the class is \\(\square\\) inches. (type an integer or a decimal. do not round.)

Explanation:

Step1: Find the total height of 15 students

The formula for the mean $\bar{x}$ is $\bar{x}=\frac{\sum x}{n}$, where $\sum x$ is the sum of the data values and $n$ is the number of data values. We know that for $n = 15$ students, the mean $\bar{x}=68.0$ inches. So we can find the total height of 15 students by rearranging the formula: $\sum x=\bar{x}\times n$. Substituting the values, we get $\sum x = 68.0\times15$.
Calculating that: $68.0\times15 = 1020$ inches.

Step2: Find the total height of 16 students

Now, we add Danielle's height (71.2 inches) to the total height of the 15 students. So the new total height $\sum x_{new}=1020 + 71.2$.
Calculating that: $1020+71.2 = 1091.2$ inches.

Step3: Find the mean height of 16 students

Now we use the mean formula again with $n = 16$ and the new total height $\sum x_{new}=1091.2$. So the new mean $\bar{x}_{new}=\frac{\sum x_{new}}{16}$. Substituting the values, we get $\bar{x}_{new}=\frac{1091.2}{16}$.
Calculating that: $\frac{1091.2}{16}=68.2$ inches.

Answer:

68.2