Given the population data set $3,1,2,9,5$, what is the standard deviation of this population (rounded to two decimal places)?

• A. $2.83$
• B. $2.97$
• C. $3.41$
• D. $3.16$

Answer: (B)

Verified step by step guidance

1. First, calculate the mean (average) of the population data set. Use the formula: \[\text{mean} = \frac{\sum_{i=1}^N x_i}{N}\] where \(x_i\) are the data points and \(N\) is the total number of data points.
2. Next, find the squared differences between each data point and the mean. For each data point \(x_i\), compute: \[ (x_i - \text{mean})^2 \]
3. Then, calculate the average of these squared differences. Since this is a population, divide the sum of squared differences by \(N\): \[ \text{variance} = \frac{\sum_{i=1}^N (x_i - \text{mean})^2}{N} \]
4. Finally, take the square root of the variance to find the population standard deviation: \[ \text{standard deviation} = \sqrt{\text{variance}} \]
5. Round the resulting standard deviation to two decimal places as requested.