Question

the data set 80, 84, 79, 44, 87, 73, 89, 90, 82, 89, 93, 97, 77, and 71 is graphed below. use the histogram to answer the questions. what type of distribution is this? what is the mean? what is the median? which measure of center is the best choice for this data set?

Explanation:

Step1: Calculate the mean

The mean formula is $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here $n = 14$, and $\sum_{i=1}^{14}x_{i}=80 + 84+79+44+87+73+89+90+82+89+93+97+77+71=1125$. So $\bar{x}=\frac{1125}{14}\approx80.36$.

Step2: Find the median

First, order the data set: $44,71,73,77,79,80,82,84,87,89,89,90,93,97$. Since $n = 14$ (an even - numbered data set), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th values. $\frac{n}{2}=7$ and $\frac{n}{2}+1 = 8$. The 7th value is $82$ and the 8th value is $84$. So the median is $\frac{82 + 84}{2}=83$.

Step3: Determine the distribution type

The data is concentrated around the $80 - 89$ interval, with tails on both sides. This is a symmetric distribution.

Step4: Choose the best measure of center

Since the distribution is symmetric, both the mean and the median are good measures of center. But the mean takes into account all values in the data set, so it is a more comprehensive measure in this case.

Answer:

What type of distribution is this? Symmetric
What is the mean? Approximately 80.36
What is the median? 83
Which measure of center is the best choice for this data set? Mean