Answer:
first, arrange the numbers from least to greatest order. (Actually this is a longer step, if you also want to find the median. But since you are only asking for range and standard deviation, I won't do that here.) So, just find the lowest number and the highest number. Subtract the lowest from the highest. That is your range.
Your problem:
lowest: 98.6
highest: 131.9
subtract: 131.9 - 98.6 = 33.3 ← this is your range
Now, standard deviation.
Standard deviation is the amount of variety you have in your data sample.
Step 1: Find the mean
Add up all your numbers and divide by how many numbers you have.
You have 10 numbers in your sample.
115.6 + 109.3 + 126 + 104.9 + 131.9 + 113.7 + 119.8 + 98.6 + 131.9 + 131.9
total = 1,183.6
now divide this by 10. (n is the variable used here, so n = 10. This is because you have ten numbers. )
so n = 10
and 1,183.6/10 = 118.3
Now subtract each number by 118.3.
115.6 - 118.3 = -2.7
109.3 - 118.3 = -9
126 - 118.3 = 7.7
104.9 - 118.3 = -13.4
131.9 -118.3 = 13.6
113.7 - 118.3 = -4.6
119.8 - 118.3 = 1.5
98.6 - 118.3 = -19.7
131.9 - 118.3 = 13.6
131.9 - 118.3 = 13.6
now square all these numbers
7.29
81
59.29
179.56
184.96
21.16
0.75
388.09
184.96
184.96
Find the sum of these squares now. (We're almost done!)
sum = 1,292.02
remember our n?
it was n=10
now the formula for this is,
sum of squares ÷ n-1
substitute all this in.
1,292.02 ÷ 9 = 143.55
Remember. This is the VARIANCE. NOT the standard deviation.
The last step to find the standard deviation is, to find the square root of what we got. (143.55)
√143.55
= 11.9812353286 this is the number, but rounded two more decimal places is..
11.98 is the standard deviation.
Hope this helped!