Answer:
Step-by-step explanation:
Before we can calculate the standard deviation of the dataset, we need to get the mean value first.
mean = sum of the values/total number given
mean = -8+2+2+4+15/5
mean = 15/5
mean (xbar) = 3
For ungrouped data:
Variance S²= ∑(xi-xbar)²/N-1
xi are the individual values
xbar is the mean value = 3
N is the total number in the dataset = 5
Variance = (-8-3)²+(2-3)²+(2-3)²+(4-3)²+(15-3)²/5-1
S² = (-11)²+(-1)²+(-1)²+(1)²+(12)²/4
S² = (121+1+1+1+144)/4
S² = 67
Hence the variance of data sample is 67.00
Standard deviation is the square root of the variance.
√S² = Standard deviation
√67 = Standard deviation
Standard deviation = 8.185
Standard deviation ≈ 8.19 (to 2 decimal place)
