Question

the ages of valentinas five cousins are listed below. 8 12 6 16 15 1) calculate the mean. $mu = square$ 2) fill in the table below: fill in the differences of each data value from the mean, then the squared differences. $x$ $x - mu$ $(x - mu)^2$ 8 12 6 16 15 $sum(x - mu)^2=$ 3) calculate the population standard deviation ($sigma$). $sigma=sqrt{\frac{sum(x - mu)^2}{n}}=square$ (please round your answer to two decimal places)

Explanation:

Step1: Sum the data values

$8 + 12 + 6 + 16 + 15 = 57$

Step2: Calculate the mean

$\mu = \frac{57}{5} = 11.4$

Step3: Compute differences from mean

For $x=8$: $8 - 11.4 = -3.4$; $x=12$: $12 - 11.4 = 0.6$; $x=6$: $6 - 11.4 = -5.4$; $x=16$: $16 - 11.4 = 4.6$; $x=15$: $15 - 11.4 = 3.6$

Step4: Compute squared differences

$(-3.4)^2=11.56$; $(0.6)^2=0.36$; $(-5.4)^2=29.16$; $(4.6)^2=21.16$; $(3.6)^2=12.96$

Step5: Sum squared differences

$11.56 + 0.36 + 29.16 + 21.16 + 12.96 = 75.2$

Step6: Calculate population standard deviation

$\sigma = \sqrt{\frac{75.2}{5}} = \sqrt{15.04} \approx 3.88$

Answer:

1. 11.4

2)

x	x - μ	(x - μ)²
12	0.6	0.36
6	-5.4	29.16
16	4.6	21.16
15	3.6	12.96
	Σ(x - μ)² =	75.2

1. 3.88