Variance Calculation of Daily Water Consumption

A research team conducted a study on the daily water consumption of individuals across different age groups. The data was compiled into a table showing the average daily consumption (in liters) for five different age categories:

Based on the findings, the research team is interested in understanding how daily water consumption trends vary with age, specifically analyzing the variance in water consumption across these age groups. They computed the variance and found the following results:

Let the average daily consumption for the age groups be represented by $x_1, x_2, x_3, x_4, x_5$. Given that:

• $x_1 = 1.5$
• $x_2 = 2.0$
• $x_3 = 2.5$
• $x_4 = 2.0$
• $x_5 = 1.8$

Which of the following represents the calculated variance for daily water consumption? Use the formula for variance:

$Var(X) =\frac{1}{N} imes igg( extstyleigsum_{i=1}^{N} ig(x_i - ar{x}ig)^2 igg)$ where $N$ is the total number of observations and $ar{x}$ is the average consumption.