Respuesta :
Answer:
The sample standard deviation of 5.95.9 inches differs from the population standard deviation of 5.25.2 inches because of their formulas for calculating it.
Step-by-step explanation:
We are given the heights, in inches, of the starting five players on a college basketball team ;
68, 73, 77, 75 and 84
Now whether we treat this data as sample data or population data, the mean height would remain same in both case because the formula for calculating mean is given by ;
Mean = Sum of all data values ÷ No. of observations
Mean = ( 68 + 73 + 77 + 75 + 84 ) ÷ 5 = 75.4 inches
So, numerically, the sample mean of 75.4 inches is the same as the population mean.
Now, coming to standard deviation there will be difference in both sample and population standard deviation and that difference occurs due to their formulas;
Formula for sample standard deviation = [tex]\frac{\sum (X_i - Xbar)^{2} }{n-1}[/tex]
where, [tex]X_i[/tex] = each data value
X bar = Mean of data
n = no. of observations
Sample standard deviation = [tex]\frac{ (68 - 75.4)^{2} +(73 - 75.4)^{2}+(77- 75.4)^{2}+(75- 75.4)^{2}+(84 - 75.4)^{2} }{5-1}[/tex]
= 5.9 inches
Whereas, Population standard deviation = [tex]\frac{\sum (X_i - Xbar)^{2} }{n}[/tex]
= [tex]\frac{ (68 - 75.4)^{2} +(73 - 75.4)^{2}+(77- 75.4)^{2}+(75- 75.4)^{2}+(84 - 75.4)^{2} }{5}[/tex] = 5.2 inches .
So, that's why sample standard deviation of 5.95.9 inches differs from the population standard deviation of 5.25.2 inches only because of formula.
