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 = $\frac{\sum (X_i - Xbar)^{2} }{n-1}$

where, $X_i$ = each data value

X bar = Mean of data

n = no. of observations

Sample standard deviation = $\frac{ (68 - 75.4)^{2} +(73 - 75.4)^{2}+(77- 75.4)^{2}+(75- 75.4)^{2}+(84 - 75.4)^{2} }{5-1}$

= 5.9 inches

Whereas, Population standard deviation = $\frac{\sum (X_i - Xbar)^{2} }{n}$

= $\frac{ (68 - 75.4)^{2} +(73 - 75.4)^{2}+(77- 75.4)^{2}+(75- 75.4)^{2}+(84 - 75.4)^{2} }{5}$ = 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.

7 0

3 years ago

Which number rounds to 260 when rounded to the nearest 10?

mylen [45]

I looked it up and got this........

What is 260 rounded to the nearest ten?
Here we will tell you what 260 is rounded to the nearest ten and also show you what rules we used to get to the answer. First, 260 rounded to the nearest ten is:
260
Remember, we did not necessarily round up or down, but to the ten that is nearest to 260.
When rounding to the nearest ten, like we did with 260 above, we use the following rules:
A) We round the number up to the nearest ten if the last digit in the number is 5, 6, 7, 8, or 9.
B) We round the number down to the nearest ten if the last digit in the number is 1, 2, 3, or 4.
C) If the last digit is 0, then we do not have to do any rounding, because it is already to the ten.

3 0

3 years ago