Question

_________ is the positive square root of the average of squared differences of each value from the mean.

• A. Mode
• B. Variance
• C. Median
• D. Standard Deviation

Answer 1

The Correct Option is D

The term that is the positive square root of the average of squared differences of each value from the mean is called the Standard Deviation.

Here's why: to compute the standard deviation, follow these steps: 

• Calculate the mean (average) of the data set.
• Subtract the mean from each value in the data set and square the result (the squared difference).
• Find the average of these squared differences; this is known as the variance.
• The standard deviation is the positive square root of the variance.

Therefore, the correct answer is Standard Deviation.

Answer 2

(1) Mode: The mode is the value that appears most frequently in a dataset. It is not related to the square root of squared differences.

(2) Variance: Variance measures the average squared difference of each value from the mean. While it is part of the calculation, it's not the square root.

(3) Median: The median is the middle value in a sorted dataset. It is not related to the square root of squared differences.

(4) Standard Deviation: The standard deviation is the positive square root of the variance. It represents the spread of data around the mean.

Therefore, (4) Standard Deviation is the positive square root of the average of the squared difference of each value from the mean.