2 1 B Weighted Mean

When calculating statistics and data values are repeated and listed with their frequencies, a weighted mean must be calculated. The frequency 'f' denotes how often a value occurs and slightly changes the formulas for calculating the mean.

The formula for the population parameter mu (μ) is the sum of (X values times frequencies) divided by the sum of frequencies. Similarly, for the sample mean (X-bar), it's the sum of (Xs times frequencies) divided by the sum of frequencies.

Using an example of speeding tickets, the video demonstrates data listed with frequencies: one ticket (3 people), two tickets (2 people), three tickets (1 person), and four tickets (5 people). This condensed data set is used to calculate the mean directly with the weighted mean formula.

To apply the formula, a new column is created for 'x times frequency'. Each x-value is multiplied by its frequency: 1*3=3, 2*2=4, 3*1=3, 4*5=20. The sum of this column (3+4+3+20) is 30.

The sum of the frequencies (3+2+1+5) is 11. To find the weighted mean (X-bar), the sum of (x times frequency) (30) is divided by the sum of frequencies (11), resulting in approximately 2.7. This method is often quicker and easier for data with repeated values.