Raymond B. answered • 06/29/19
Math, microeconomics or criminal justice
It's easy to make a mistake if you're doing these calculations by hand. There are on line calculations that will spit out the answers in a micro second if you just type in those 10 numbers. Or use a hand calculator with statistics functions.
Answer is
mean=1.237 or rounded off to two decimal places: 1.24
variance = 0.028666 rounded off to 6 decimal places or 0.03 for 2 decimal places
The online statistics calculators also give you the standard deviation as 0.1693 The standard deviation is just the square root of the variance.
If you want to work this out by hand, just add the 10 numbers and divide the sum by 10. That gives 1.237 as the mean
Then subtract each of the ten numbers individually from the mean. Square each of those differences and sum them. Then divide by 10. That gives the variance if 10 comprises the population, but if the 10 values are a sample of larger population, divide by 9. n=10 n-1=9 n is the number of data points.
Even with a calculator summing and squaring, you can easily punch in a slightly wrong number. Try a couple online calculators. If they agree, you probably have the right answer.
Also just look to see if the answer is in the ball park. The mean looks right, about the middle of all ten numbers. One way to check the variance is see if about 95% or most all the values are within 2 standard deviations of the mean. For this case, 2 standard deviations is about 0.34 1.24 plus or minus 0.34 is 0.90 to 1.58 90% or 9 out of 10 of the values are within that range, so it's at least fairly close to the actual standard deviation and variance. If the values are normally distributed about 95% of all the values should be within 2 standard deviations of the mean. But for less than 30 data points, statisticians usually use the t distribution rather than the z tables and normal distribution, but they're fairly close for most values.
