3 Complete the table and determine the standard deviation of the ten items listed, correct to
two decimal places.
σ2
=
∑(x - x̄ )2
______ n
x x – x̄ (x – x̄ )2
5 5 – 7 = – 2 4
13 13 – 7 = 6 36
6 6 – 7 = – 1 1
To find the standard deviation, we need to calculate the variance first. The variance is given by the formula:
σ^2 = Σ(x - x̄)^2 / n
where Σ denotes the sum of the values, n is the number of values, x is the individual value, and x̄ is the mean of the values.
Using the provided table, we can calculate the variance as follows:
σ^2 = ((-2)^2 + 6^2 + (-1)^2) / 3
σ^2 = (4 + 36 + 1) / 3
σ^2 = 41 / 3
To find the standard deviation, we simply take the square root of the variance:
σ = √(41 / 3)
Using a calculator, we get:
σ ≈ 3.08 (rounded to two decimal places)