Urgent! Standard Deviation Algebra 2 Problem!!

Question

I keep getting different answers each time I solve this... help, please!

Precipitation (in inches per year): 9.4, 17.0, 7.3, 7.0, 16.1, 5.4, 6.9, 8.5, 4.2, 9.2

1. Find the standard deviation. (Answer choices: 3.95, 4.33, 9.1, 4.0)
2. How many years was the rainfall more than one standard deviation from the mean? (Answer choices: 1, 2, 3, 4)

Each time I try to find the standard deviation, I have got either 27.3, which is nowhere near at all, or 4.24. I am really just stuck and don't know what to do.

Thanks in advance!

Answer 1

1)

Adding all the data values, ∑x_i=91

μ = ∑x_i/n = 91/10 = 9.1 for n = 10

For σ = √(∑(x_i-μ)²/n) =4.02566 ≈ 4.0

2) More than one standard deviation > σ + μ = 4 + 9.1 = 13.1

Looks like only two years were greater than 13.1 inches of rain. (17 and 16.1)

The answer is 2.

Answer 2

The mean is 9.1. I also get 4.24 for standard deviation, if we assume the data is a sample. If we consider this data set the entire population, then the standard deviation is 4.03, which would be close to one of the possible choices. More than 1 standard deviation from the mean would be values outside of 9.1 +/- 4.0 = 5.1, 13.1. 4.2, 17.0 and 16.1 are outside that range.(3).