Question

find the mean, median, and mode of the following data set. round answers to two decimal places if needed.
32, 30, 102, 33, 28, 26, 32, 26
a. the mean is
b. the median is
c. for mode, if there is more than one number, separate the numbers with a \,\ e.g. 100,121.
d. the mode is

Explanation:

Step1: Calculate the mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here, $n = 8$ and $\sum_{i=1}^{8}x_{i}=32 + 30+102 + 33+28+26+32+26=309$. So, $\bar{x}=\frac{309}{8}=38.625\approx38.63$.

Step2: Calculate the median

First, sort the data set: $26,26,28,30,32,32,33,102$. Since $n = 8$ (even), the median $M=\frac{x_{\frac{n}{2}}+x_{\frac{n}{2}+1}}{2}$. Here, $x_{4}=30$ and $x_{5}=32$. So, $M=\frac{30 + 32}{2}=31$.

Step3: Calculate the mode

The mode is the number that appears most frequently. In the data set $26$ appears $2$ times and $32$ appears $2$ times.

Answer:

a. The mean is $38.63$
b. The median is $31$
c. The mode is $26,32$