The mean, also known as the average, is the sum of all the observations divided by the number of observations. In this case, the mean of 5 observations is given as 4.80. Mathematically, we can represent this as:

(x1 + x2 + x3 + x4 + x5) / 5 = 4.80

where x1, x2, x3, x4, and x5 are the 5 observations.

We can simplify this equation to:

x1 + x2 + x3 + x4 + x5 = 24

This means that the sum of all 5 observations is 24.


The variance is a measure of how spread out the observations are from the mean. It is calculated by taking each observation, subtracting the mean, squaring the result, and then summing all of these squared differences. The sum is then divided by the number of observations minus 1. In this case, the variance of 5 observations is given as 6.16. Mathematically, we can represent this as:

[(x1 - 4.80)^2 + (x2 - 4.80)^2 + (x3 - 4.80)^2 + (x4 - 4.80)^2 + (x5 - 4.80)^2] / 4 = 6.16

where x1, x2, x3, x4, and x5 are the 5 observations.

We can simplify this equation to:

(x1^2 + x2^2 + x3^2 + x4^2 + x5^2) - (24 x 4.80) + (4 x 4.80^2) = 24 x 6.16

This means that the sum of the squares of the 5 observations minus 24 times the mean plus 4 times the square of the mean is equal to 24 times the variance.


In conclusion, we have calculated the mean and variance of 5 observations given as 4.80 and 6.16, respectively. The mean is equal to the sum of all observations divided by the number of observations, while the variance is a measure of how spread out the observations are from the mean. By calculating these values, we can better understand the distribution of the observations and make more informed decisions based on the data.