Question

rohan tracks his total expenses for a year, and the data list is: (200, 180, 190, 210, 200, 195, 205, 100, 185, 105, 200, 210). the mean is the median is

Explanation:

Step1: Calculate the mean

The formula for 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.
First, find the sum of the data: $200 + 180+190 + 210+200+195+205+100+185+105+200+210=\sum_{i = 1}^{12}x_{i}=2280$.
The number of data - points $n = 12$.
So, $\bar{x}=\frac{2280}{12}=190$.

Step2: Calculate the median

Arrange the data in ascending order: $100,105,180,185,190,195,200,200,200,205,210,210$.
Since $n = 12$ (an even number), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered data - points.
$\frac{n}{2}=6$ and $\frac{n}{2}+1 = 7$.
The 6th value is $195$ and the 7th value is $200$.
Median $=\frac{195 + 200}{2}=197.5$.

Answer:

The mean is 190.
The median is 197.5.