Question

find the mean, median, and mode of the following data:
(round to 1 decimal place as needed)
34, 15, 25, 32, 15, 26, 33, 15, 26, 21
a. mean =
b. median =
c. mode =
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Explanation:

Step1: Calculate the mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here, $n = 10$ and $\sum_{i=1}^{10}x_{i}=34 + 15+25+32+15+26+33+15+26+21=242$. Then $\bar{x}=\frac{242}{10}=24.2$.

Step2: Find the median

First, sort the data: $15,15,15,21,25,26,26,32,33,34$. Since $n = 10$ (even), the median $M=\frac{x_{\frac{n}{2}}+x_{\frac{n}{2}+1}}{2}$. Here, $x_{5}=25$ and $x_{6}=26$, so $M=\frac{25 + 26}{2}=25.5$.

Step3: Determine the mode

The mode is the value that appears most frequently. In the data set $15,15,15,21,25,26,26,32,33,34$, the number $15$ appears $3$ times (more frequently than other numbers).

Answer:

a. Mean = $24.2$
b. Median = $25.5$
c. Mode = $15$