Calculating Standard Deviation, Mean, and Variance of Grouped Data

What is the first step in finding the standard deviation, variance, and mean for grouped data?

• Sum the frequencies

• Square the deviations

• Find the interval midpoints

• Calculate the total frequency

How do you calculate the interval midpoint for a given data interval?

• Divide the larger number by the smaller number

• Add the two numbers and divide by two

• Multiply the two numbers

• Subtract the smaller number from the larger number

What is the next step after finding the interval midpoints?

• Add the midpoints together

• Multiply the midpoints by their corresponding frequencies

• Square the midpoints

• Subtract the midpoints from the mean

What does the symbol Σ (Sigma) represent in the context of this tutorial?

• Multiplication

• Subtraction

• Division

• Summation

How is the mean (x-bar) calculated for grouped data?

• Sum of the products of midpoints and frequencies divided by the total frequency

• Sum of midpoints divided by the number of intervals

• Sum of squared deviations divided by the total frequency

• Sum of frequencies divided by the number of intervals

What is the next step after calculating the mean?

• Square the mean

• Add the mean to each midpoint

• Multiply the mean by each frequency

• Subtract the mean from each midpoint

What do you do after subtracting the mean from each midpoint?

• Add the results together

• Divide the results by the total frequency

• Multiply the results by the frequencies

• Square the results

How is the variance (s^2) calculated?

• Sum of squared deviations divided by the total frequency

• Sum of squared deviations times frequencies divided by n-1

• Sum of deviations divided by the total frequency

• Sum of deviations times frequencies divided by n-1

What is the formula for standard deviation?

• Sum of the deviations

• Sum of the squared deviations

• Square of the variance

• Square root of the variance

What is the final step in finding the standard deviation?

• Add the squared deviations together

• Divide the sum of squared deviations by the total frequency

• Multiply the sum of squared deviations by the total frequency

• Take the square root of the variance