Question

for the following list of data, calculate (a) the mean, (b) the median, and (c) the mode or modes (if any). 133, 135, 147, 131, 147, 136 (a) the mean is . (round to the nearest tenth as needed.)

Explanation:

Step1: Calculate sum of data

$133 + 135+147+131+147+136=829$

Step2: Calculate number of data points

There are 6 data - points, $n = 6$.

Step3: Calculate the mean

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}=\frac{829}{6}\approx138.2$

Step4: Arrange data in ascending order

$131,133,135,136,147,147$

Step5: Calculate the median

Since $n = 6$ (even), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered data points. $\frac{n}{2}=3$ and $\frac{n}{2}+1 = 4$. So, median$=\frac{135 + 136}{2}=\frac{271}{2}=135.5$

Step6: Find the mode

The mode is the data - point that appears most frequently. Here, 147 appears 2 times and other numbers appear once, so the mode is 147.

Answer:

(a) The mean is $138.2$.
(b) The median is $135.5$.
(c) The mode is $147$.