Respuesta :
Let's recall the formulas for getting the different values:
[tex]x\text{ bar = }\bar{x}\text{ = }\frac{\Sigma x}{n}[/tex][tex]\text{Sum of the square deviations = }\Sigma(\text{x - }\bar{\text{x}})^2[/tex][tex]\text{Population variance = }\frac{\Sigma(\text{x - }\bar{\text{x}})^2}{n}[/tex]A.) Let's now get the x bar (mean):
[tex]x\text{ bar = }\bar{x}\text{ = }\frac{\Sigma x}{n}[/tex][tex]\bar{x}\text{ = }\frac{10\text{ + 15 + 16 + 16 + 16 + 19 + 25}}{7}\text{ = }\frac{117}{7}=\text{ 16.7142857143 }\approx\text{ 16.7}[/tex]B.) Let's get the sum of the square deviations:
[tex]\text{Sum of the square deviations = }\Sigma(\text{x - }\bar{\text{x}})^2[/tex][tex]\text{ = (10-16.7)}^2+(15-16.7)^2+(16-16.7)^2(3)+(19-16.7)^2+(25-16.7)^2[/tex][tex]=44.9\text{ + 2.9 + (0.5)(3) + 5.3 + 68.9}[/tex][tex]=44.9\text{ + 2.9 + 1.5 + 5.3 + 68.9}[/tex][tex]\Sigma(\text{x - }\bar{\text{x}})^2\text{ = 123.5}[/tex]C.) Let's get the population variance:
[tex]\text{Population variance = }\frac{\Sigma(\text{x - }\bar{\text{x}})^2}{n}\text{ ; but }\Sigma(\text{x - }\bar{\text{x}})^2\text{ = 123.40 and n = 7}[/tex][tex]\frac{\Sigma(\text{x - }\bar{\text{x}})^2}{n}\text{ = }\frac{123.5}{7}[/tex][tex]\frac{\Sigma(\text{x - }\bar{\text{x}})^2}{n}\text{ = 17.64285714286 }\approx\text{ 17.60}[/tex]