Question

rohan tracks his total expenses for a year, and the data list is: {200, 180, 190, 210, 200, 195, 205, 190, 185, 195, 200, 210}. the mean is <box> <. the median is <box> <.

Explanation:

Step1: Sort the data

The sorted data set is $\{180, 185, 190, 190, 195, 195, 200, 200, 200, 205, 210, 210\}$. There are $n = 12$ data - points.

Step2: Calculate the median

Since $n$ is even, the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered data - points. $\frac{n}{2}=6$ and $\frac{n}{2}+1 = 7$. The 6th value is $195$ and the 7th value is $200$. So, the median $M=\frac{195 + 200}{2}=197.5$.

Step3: Calculate the mean

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. $\sum_{i=1}^{12}x_{i}=180+185 + 190+190+195+195+200+200+200+205+210+210=2360$. Then $\bar{x}=\frac{2360}{12}\approx196.67$.

Answer:

The median is $197.5$, the mean is approximately $196.67$.