Question

find the mean, median, and mode of the following data set. round answers to two decimal places if needed.
33, 31, 99, 35, 28, 26, 33, 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 $\sum_{i=1}^{8}x_{i}=33 + 31+99+35+28+26+33+26=311$. So, $\bar{x}=\frac{311}{8}=38.875\approx38.88$.

Step2: Find the median

First, order the data set: $26,26,28,31,33,33,35,99$. Since $n = 8$ (even), the median $M=\frac{x_{\frac{n}{2}}+x_{\frac{n}{2}+1}}{2}$. Here, $x_{4}=31$ and $x_{5}=33$. So, $M=\frac{31 + 33}{2}=32$.

Step3: Determine the mode

The mode is the number that appears most frequently. The number $26$ appears $2$ times and $33$ appears $2$ times.

Answer:

a. The mean is $38.88$
b. The median is $32$
c. The mode is $26,33$