Question

unit 4 test: graphs and describing distributions multiple choice
determine the mean and the median of the data set below (round to 2 decimal places). then, determine the distribution of the data.
{1, 5, 9, 13, 17, 95, 91, 87, 83, 79}
mean:
median:
distribution (only type ls, rs or s)?

Explanation:

Step1: Calculate the mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here, $n = 10$ and $\sum_{i=1}^{10}x_{i}=1 + 5+9+13+17+95+91+87+83+79$.
$\sum_{i = 1}^{10}x_{i}=1 + 5+9+13+17+95+91+87+83+79=480$.
$\bar{x}=\frac{480}{10}=48.00$.

Step2: Calculate the median

First, order the data set: $\{1,5,9,13,17,79,83,87,91,95\}$.
Since $n = 10$ (even), the median $M=\frac{x_{\frac{n}{2}}+x_{\frac{n}{2}+1}}{2}$.
$x_{5}=17$ and $x_{6}=79$.
$M=\frac{17 + 79}{2}=\frac{96}{2}=48.00$.

Step3: Determine the distribution

In a left - skewed (LS) distribution, the mean is less than the median. In a right - skewed (RS) distribution, the mean is greater than the median. In a symmetric (S) distribution, the mean is approximately equal to the median.
Here, mean $=48.00$ and median $=48.00$.

Answer:

Mean: $48.00$; Median: $48.00$; Distribution: $S$