Variance= N ∑(Midpoint−Mean) 2 ×Frequency ​ change to number example

Sure, let's break down the formula for variance and apply it to a numerical example.

The formula for variance is:

Variance = ∑((Midpoint - Mean)² * Frequency) / N

Where:

• Midpoint is the middle value of each interval.
• Mean is the average of all midpoints.
• Frequency is the number of occurrences of each midpoint.
• N is the total number of data points.

Let's say we have the following data:

First, we calculate the midpoints for each interval:

1.5, 3.5, 5.5

Then, we calculate the mean of the midpoints:

Mean = (1.52 + 3.53 + 5.5*5) / (2+3+5) = 4.2

Next, we calculate the squared difference from the mean for each midpoint and multiply by the frequency:

(1.5 - 4.2)² * 2 = 14.44 (3.5 - 4.2)² * 3 = 0.63 (5.5 - 4.2)² * 5 = 8.55

Finally, we sum these values and divide by N (the total number of data points, which is 2+3+5=10) to get the variance:

Variance = (14.44 + 0.63 + 8.55) / 10 = 2.36