Find the sample variance for the following data set

Asked by maham237 @ 12/02/2021 in Mathematics viewed by 289 People

Calculate the range, population variance, and population standard deviation for the following data set. If necessary, round to one more decimal place than the largest number of decimal places given in the data.

Answered by maham237 @ 12/02/2021

Answer:

$Range = 11-2=9$

$\mu = \frac{2+3+4+5+6+7+8+9+10+11}{10}=6.5$

$\sigma^2 =8.25 \approx 8.3$

$\sigma = \sqrt{8.25}= 2.87 \approx 2.9$

Step-by-step explanation:

Assuming this question: "Calculate the range, population variance, and population standard deviation for the following data set. If necessary, round to one more decimal place than the largest number of decimal places given in the data. 2,3,4,5,6,7,8,9,10,11
"

Solution to the problem

The range is defined as $Range = Max -Min$ and if we replace we got:

$Range = 11-2=9$

Now we can calculate the population mean with this formula:

$\mu =\frac{\sum_{i=1}^n X_i}{N}$

And if we replace we got:

$\mu = \frac{2+3+4+5+6+7+8+9+10+11}{10}=6.5$

The population variance is given by:

$\sigma^2 = \frac{\sum_{i=1}^n (X_i -\mu)^2}{N}$

And after replace we got: $\sigma^2 =8.25 \approx 8.3$

And the population standard deviation would be just the square root of the variance and we got:

$\sigma = \sqrt{8.25}= 2.87 \approx 2.9$

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