Question

1. calculate the mean. μ = 12.2 2) fill in the table below: fill in the differences of each data value from the mean, then the squared differences. x x - μ (x - μ)² 8 -4.2 17.64 16 3.8 14.44 17 4.8 23.04 6 -6.2 38.44 14 1.8 3.24 ∑(x - μ)² = 96.8 3) calculate the population standard deviation (σ). σ = √(∑(x - μ)² / n) = (please round your answer to two decimal places) enter an integer or decimal number (more...) submit question

Explanation:

Step1: Identify values

We know that $\sum(x - \mu)^2=96.8$ and assume the number of data - points $N = 5$ (since there are 5 data values: 8, 16, 17, 6, 14).

Step2: Apply standard - deviation formula

The formula for population standard deviation is $\sigma=\sqrt{\frac{\sum(x - \mu)^2}{N}}$. Substitute $\sum(x - \mu)^2 = 96.8$ and $N = 5$ into the formula: $\sigma=\sqrt{\frac{96.8}{5}}=\sqrt{19.36}$.

Step3: Calculate the result

$\sqrt{19.36}=4.40$

Answer:

$4.40$