Question

compute the range and sample standard deviation for strength of the concrete (in psi).
3980, 4140, 3300, 3100, 2920, 3870, 4140, 4020

the range is 1220 psi.
( s = square ) psi (round to one decimal place as needed.)

Explanation:

Step1: Confirm range (given)

Range = Max - Min = $4140 - 2920 = 1220$

Step2: Calculate sample mean

First, sum all values:
$3980 + 4140 + 3300 + 3100 + 2920 + 3870 + 4140 + 4020 = 29470$
Sample size $n=8$, so mean:
$\bar{x} = \frac{29470}{8} = 3683.75$

Step3: Compute squared deviations

Calculate $(x_i - \bar{x})^2$ for each value:
$(3980-3683.75)^2 = 296.25^2 = 87764.0625$
$(4140-3683.75)^2 = 456.25^2 = 208164.0625$
$(3300-3683.75)^2 = (-383.75)^2 = 147264.0625$
$(3100-3683.75)^2 = (-583.75)^2 = 340764.0625$
$(2920-3683.75)^2 = (-763.75)^2 = 583314.0625$
$(3870-3683.75)^2 = 186.25^2 = 34689.0625$
$(4140-3683.75)^2 = 456.25^2 = 208164.0625$
$(4020-3683.75)^2 = 336.25^2 = 113064.0625$

Step4: Sum squared deviations

Sum = $87764.0625 + 208164.0625 + 147264.0625 + 340764.0625 + 583314.0625 + 34689.0625 + 208164.0625 + 113064.0625 = 1723187.5$

Step5: Calculate sample variance

Variance $s^2 = \frac{\text{Sum of squared deviations}}{n-1} = \frac{1723187.5}{7} \approx 246169.6429$

Step6: Find sample standard deviation

Take square root of variance:
$s = \sqrt{246169.6429} \approx 496.15$

Answer:

The range is 1220 psi.
$s = 496.2$ psi