Mean Deviation

We are given the following information: - The mean of 5 observations is 4.4 - The variance of 5 observations is 8.24 - Three of the observations are 1, 2, and 6. Let the five observations be , , , and the unknown observations be and . Step 1: Use the formula for the mean The formula for the mean of a set of observations is: Substitute the known values: Multiply both sides by 5: Step 2: Use the formula for the variance The formula for the variance is: Where is the mean. We are given the variance as 8.24, and . Substituting the values, we get: Simplify the terms: Substitute these into the variance equation: Multiply both sides by 5: Step 3: Solve for and We already know that . Let’s check for values of and that satisfy both and the variance equation. After testing possible pairs, we find that the values and satisfy both conditions. Thus, the other two observations are and . The correct answer is option (1), 9, 4.

The standard deviation measures the spread of data, which is unaffected by a constant shift. If each number is increased by 5, the mean changes, but the standard deviation remains the same. Given the original standard deviation is 2: To confirm, recall that standard deviation is calculated as: If each is increased by 5, the new values are , and the new mean is . The deviations become: Thus, the standard deviation remains unchanged. The new standard deviation is: