Given the data set $0.40$, $0.72$, $1.15$, $2.14$, what is the variance of the data set? Round your answer to the nearest hundredth.

• A. $0.77$
• B. $0.49$
• C. $0.68$
• D. $0.59$

Answer: (D)

Verified step by step guidance

1. Step 1: Calculate the mean (average) of the data set. Use the formula: \[\text{mean} = \frac{\sum x_i}{n}\] where \(x_i\) are the data points and \(n\) is the number of data points.
2. Step 2: Find the squared differences between each data point and the mean. For each data point \(x_i\), compute \[ (x_i - \text{mean})^2 \].
3. Step 3: Sum all the squared differences obtained in Step 2.
4. Step 4: Since this is a sample variance problem (assuming the data set is a sample), divide the sum of squared differences by \(n - 1\), where \(n\) is the number of data points. The formula for sample variance is: \[ s^2 = \frac{\sum (x_i - \text{mean})^2}{n - 1} \].
5. Step 5: Round the resulting variance to the nearest hundredth as requested.