Question

guys please answer this
class X statistics​

Answer 1

Answer:

the mean is 50.1 while the median is 52 as it remains unchanged.

Step-by-step explanation:

The mean is just taking the sum of observations divided by the number of observations. Hence, the mean $\bar x$ is given by

$\bar x = \frac{x_1 +x_2 + \dots + x_{99} + 100}{100}$.

As we know only the last greatest observation changed from 100 to 110

then we know that the mean should actually be

$\bar x' = \frac{x_1+x_2+\dots+x_{99}+110}{100} = \frac{(x_1+x_2+\dots+x_{99}+100) + 10}{100} = \frac{x_1+x_2+\dots+x_{99}+100}{100} + \frac{10}{100}$

We then notice that this is just the same as

$\bar x' = \bar x + \frac{10}{100} = 50+0.1=50.1$.

As the median is the 'middle' observation in the set (list) of observations

then merely increasing the value of the greatest observation does not change what the 'middle' observation is. Therefore the median stays the same.