Questions: Consider the following data: 10, 15, 9, 12, 14, 6 Step 1 of 3: Calculate the value of the sample variance. Round your answer to one decimal place.

Transcript text: Consider the following data: \[ 10,15,9,12,14,6 \] Step 1 of 3: Calculate the value of the sample variance. Round your answer to one decimal place. Answer How to enter your answer (opens in new window)

Solution

Solution Steps

Step 1: Calculate the sample mean

The sample mean \(\bar{x}\) is calculated as \(\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}\), where \(n\) is the total number of data points. For our dataset, this is \(\bar{x} = 11\).

Step 2: Calculate the deviations from the mean for each data point

For each data point \(x_i\), we calculate the deviation from the mean as \(x_i - \bar{{x}}\).

Step 3: Square each deviation

Each deviation from the mean is squared to ensure positive and negative deviations do not cancel each other out: \((x_i - \bar{{x}})^2\).

Step 4: Sum all squared deviations

All squared deviations are summed: \(\sum_{{i=1}}^{{n}} (x_i - \bar{{x}})^2\).

Step 5: Divide by \(n-1\)

The sum of squared deviations is divided by \(n-1\) to find the sample variance: \(s^2 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{n-1}\), which gives us \(s^2 = 11.2\).