Question

A recent survey of a new diet cola reported the following percentages of people who liked the taste. Find the weighted mean of the percentages. Remember that the x values in your equation are the ones that you are trying to find the weighted mean of. You are trying to find the average percentage of people who prefer the taste of the new diet cola. Area % Favored Number Surveyed
1 40 1000
2 30 3000
3 50 800

Answer 1

Answer:

35.41%

Step-by-step explanation:

The average weighted mean is a mean that is calculated by multiplying the probability of an event by its quantitative outcome and then summing all the products and dividing this result by the number of people surveyed. We use this mean when not all the data has the same weight (some of them contribute more than others)

1. To find the weighted mean of this data, we are going to multiply the percentage of people who liked the new diet cola by the number surveyed.

40 x 1000 = 40,000

30 x 3000= 90,000

50 x 800 = 40,000

    2. Now we are going to sum these results

40,000 + 90,000 + 40,000 = 170,000

     3. The total of people who were surveyed is:

1000 + 3000 + 800 = 4800.

   4. Dividing the sum of the products by the number of people we get:

$\frac{170000}{4800} = 35.41$

Therefore, the average percentage of people who prefer the taste of the new diet coke is 35.41%