Final answer:
To calculate the population standard deviation of the given data set (36, 16, 31, 17, 24), find the mean, subtract the mean from each data point and square the result, sum up these squared differences.
Step-by-step explanation:
To find the population standard deviation for the data set 36, 16, 31, 17, 24, follow these steps:
Calculate the mean (average) of the data set.
Subtract the mean from each data point and square the result (the squared difference).
Sum up all the squared differences.
Divide this sum by the number of data points (since we seek the population standard deviation, not the sample standard deviation).
Take the square root of the result which gives the population standard deviation.
Let's perform the calculation:
Mean = (36 + 16 + 31 + 17 + 24) / 5 = 124 / 5 = 24.8
Squared differences = (11.2² + (-8.8)² + 6.2² + (-7.8)² + (-0.8)²)
Sum of squared differences = 125.44 + 77.44 + 38.44 + 60.84 + 0.64 = 302.8
Divide by the number of data points (N = 5): Variance = 302.8 / 5 = 60.56
Population standard deviation = √60.56 = 7.7832
The population standard deviation is approximately 7.78.