Find the weighted average of a data set where 10 has a weight of 5, 30 has a weight of 3, and 50 has a weight of 2.

Kyran Hudson

Kyran Hudson

Answered question

2021-02-18

Find the weighted average of a data set where 10 has a weight of 5, 30 has a weight of 3, and 50 has a weight of 2.

Answer & Explanation

odgovoreh

odgovoreh

Skilled2021-02-19Added 107 answers

The given data set are 10 has a weight of 5, 30 has a weight of 3, and 50 has a weight of 2.
We are interest to find the weighted average of these data set.
Weighted Average: Let us consider the set of observations x1,x2...xn with corresponding weight f1,f2...fn, then the weighted average is given by the formula
x=f1x1+f2x2++fnxnf1+f2+fn
Using this above formula the weighted average is given by
x=(105)+(303)+(502)5+3+2=24010=24
Therefore, the weighted average of the given data set is 24.

user_27qwe

user_27qwe

Skilled2023-06-15Added 375 answers

To find the weighted average of a data set, we multiply each data point by its corresponding weight, sum up the results, and divide by the sum of the weights.
In this case, we have the data set: {10,30,50}, with corresponding weights: {5,3,2}.
The weighted average can be calculated as follows:
Weighted Average=(10×5)+(30×3)+(50×2)5+3+2
Simplifying the calculation:
Weighted Average=50+90+10010
Weighted Average=24010
Weighted Average=24
Therefore, the weighted average of the given data set is 24.
star233

star233

Skilled2023-06-15Added 403 answers

Step 1: Multiply each data point by its weight:
10×5=5030×3=9050×2=100
Step 2: Sum up the results:
50+90+100=240
Step 3: Divide the sum by the total weight:
2405+3+2=24010=24
Therefore, the weighted average of the given data set is 24.
karton

karton

Expert2023-06-15Added 613 answers

Result: 24
Solution:
Let's calculate the weighted average for the given data set:
Data set: 10, 30, 50
Weights: 5, 3, 2
The formula for the weighted average can be expressed as:
Weighted Average=i=1n(xi·wi)i=1nwi where xi is the data point and wi is its corresponding weight.
Substituting the values from the given data set and weights, we get:
Weighted Average=(10·5)+(30·3)+(50·2)5+3+2
Simplifying the expression:
Weighted Average=50+90+10010
Calculating the sum:
Weighted Average=24010
Therefore, the weighted average of the data set is:
Weighted Average=24
Hence, the weighted average of the given data set, with weights 5, 3, and 2 assigned to the values 10, 30, and 50 respectively, is 24.

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