91Ó°ÊÓ

Given an array of data :

$5.6,5.2,4.6,4.9,5.7\mathrm{and}6.4$

The steps for calculating the standard deviation are as follows:

Calculate the average first.

Step 2: Determine each score's standard deviation.

Step 3: Calculate the square root of each standard deviation.

Step 4: Add up the squares to get the total.

Step 5: Work out how much of a difference there is.

Step 6: Determine the square root of the variance.

$s_x=\sqrt{0.412}≈0.6419mg/dl$The number of values in the sample size is:$n=6$

The mean is calculated by dividing the total number of values by the sample size: $\overline{x}=\frac{5.6+5.2+4.6+4.9+5.7+6.4}{6}=5.4mg/dl$

If $xi$is the data values, then $(xi−\overline{x})$is the deviation ${(xi−\overline{x})}^2$the squared deviation:

The variance is calculated by dividing the sum of the squared deviations by $n-1$

${s_x}^2=\frac{0.04+0.04+0.64+0.25+0.09+1}{6-1}=\frac{2.06}{5}=0.412$

The square root of the variance is the standard deviation: $s_x=\sqrt{0.412}≈0.6419mg/dl$

Hence, the standard deviation is$0.6419mg/dl$

The phosphate level typically varies from the mean by $0.6419mg/dl$