Question

find the mean, median, and mode of the following data: (round to 1 decimal place as needed) 32, 12, 20, 28, 12, 27, 31, 12, 27, 18 mean = median = mode =

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $x_{i}$ are the data - points and $n$ is the number of data - points.
$n = 10$, and $\sum_{i=1}^{10}x_{i}=32 + 12+20 + 28+12+27+31+12+27+18=229$.
So, $\bar{x}=\frac{229}{10}=22.9$.

Step2: Calculate the median

First, order the data: $12,12,12,12,18,20,27,27,31,32$.
Since $n = 10$ (an even number), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered data - points.
$\frac{n}{2}=5$ and $\frac{n}{2}+1 = 6$.
The 5th value is $18$ and the 6th value is $20$.
Median $=\frac{18 + 20}{2}=19.0$.

Step3: Calculate the mode

The mode is the data - point that appears most frequently.
The number $12$ appears $4$ times, more frequently than any other number. So, the mode is $12$.

Answer:

Mean = $22.9$
Median = $19.0$
Mode = $12$