Question

What is the standard deviation of the data set? Round to the nearest tenth if needed. 2, 4, 7, 8, 9

Answer 1

Hiiiiiiii, okay here's the full- explanation for you, so here's the final answer. The explanation of how i got the answer is also below! Hope this helped you!!

Answer:

2.9

Step-by-step explanation:

First the mean or average = sum / data points (or N) = (2 + 4 + 7 + 8 + 9) / 5 = 6  

Now we take each of the individual values subtract the mean, and then square them, and add it all up.  

(2 - 6)^2 + (4 - 6)^2 + (7 - 6)^2 + (8 - 6)^2 + (9 - 6)^2 = 34  

Then we divide this by degrees of freedom = N - 1 to find the sample standard deviation. Note that this is different from the population standard deviation, where we would just divide N, but we use this because our data set is small, like less than 30 points.  

34 / (N - 1) -----> = 34 / (5 - 1) = 8.5  

Now, this is the variance, so we take the square root of the variance to get the sample standard deviation:  

√(8.5) = 2.9 (rounded to 1 decimal place)  

Note that scientific calculators, even my $20 version can do these kind of statistics calculations. Just enter the data set as a table of values in statistics mode, and press a few buttons, you're done!