find standard deviation for this problem
daily precip- frequency-31,1,0,2,0,1
0.oo-0.49
0.50-0.99
1.00-1.49
1.50-1.99
2.00-2.29
2.50-2.99
To find the standard deviation for this problem, you can follow these steps:
1. Calculate the mean:
- Multiply each value in the "daily precip" column by its corresponding frequency and add up all the products.
- Divide the sum by the total frequency to get the mean.
2. Calculate the variance:
- For each value in the "daily precip" column, subtract the mean from it.
- Square each result.
- Multiply each squared result by its corresponding frequency and add up all the products.
- Divide the sum by the total frequency to get the variance.
3. Calculate the standard deviation:
- Take the square root of the variance.
Let's work through an example:
Daily precip: Frequency:
0.00-0.49 31
0.50-0.99 1
1.00-1.49 0
1.50-1.99 2
2.00-2.49 0
2.50-2.99 1
Step 1: Calculate the mean:
(0.00 * 31) + (0.50 * 1) + (1.00 * 0) + (1.50 * 2) + (2.00 * 0) + (2.50 * 1) = 3.50
Total frequency = 35
Mean = 3.50 / 35 = 0.10
Step 2: Calculate the variance:
[ (0.00 - 0.10)^2 * 31 ] + [ (0.50 - 0.10)^2 * 1 ] + [ (1.00 - 0.10)^2 * 0 ] + [ (1.50 - 0.10)^2 * 2 ] + [ (2.00 - 0.10)^2 * 0 ] + [ (2.50 - 0.10)^2 * 1 ] = 1.245
Variance = 1.245 / 35 = 0.03557
Step 3: Calculate the standard deviation:
Standard deviation = √(0.03557) ≈ 0.1885
Therefore, the standard deviation for this problem is approximately 0.1885.