Calculate the weighted mean of the following data: (10, 2), (20, 3), (30, 5).

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Question: Calculate the weighted mean of the following data: (10, 2), (20, 3), (30, 5).

Options:

Correct Answer: 25

Solution:

Weighted Mean = (10*2 + 20*3 + 30*5) / (2 + 3 + 5) = 220 / 10 = 22.

Calculate the weighted mean of the following data: (10, 2), (20, 3), (30, 5).

Calculate the weighted mean of the following data: (10, 2), (20, 3), (30, 5).

Step 1: Identify the data points and their weights. The data points are (10, 2), (20, 3), and (30, 5). Here, 10, 20, and 30 are the values, and 2, 3, and 5 are their corresponding weights.
Step 2: Multiply each value by its weight. Calculate: 10 * 2 = 20, 20 * 3 = 60, and 30 * 5 = 150.
Step 3: Add the results from Step 2 together. Calculate: 20 + 60 + 150 = 230.
Step 4: Add the weights together. Calculate: 2 + 3 + 5 = 10.
Step 5: Divide the total from Step 3 by the total from Step 4 to find the weighted mean. Calculate: 230 / 10 = 23.

Weighted Mean – The weighted mean is calculated by multiplying each value by its corresponding weight, summing these products, and then dividing by the total of the weights.
Data Interpretation – Understanding how to interpret and manipulate pairs of data (value, weight) to compute the weighted mean.