Question
Download Solution PDFThe average of a group of 20 numbers is 30 and that of another group of 30 numbers is 50. What is the average of all the numbers in both the groups?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The average of a group of 20 numbers is 30
The average of another group of 30 numbers is 50.
Formula Used:
Average = Sum of all observation/Number of observation
Calculation:
Let's assume the sum of the numbers in the first group as S1 and the sum of the numbers in the second group as S2.
According to the given information, the average of the first group of 20 numbers is 30, so we have:
⇒ S1/20 = 30
⇒ S1 = 20 × 30
⇒ S1 = 600
Similarly, the average of the second group of 30 numbers is 50, so we have:
⇒ S2/30 = 50
⇒ S2 = 30 × 50
⇒ S2 = 1500
To find the average of all the numbers in both groups, we need to calculate the total sum and the total count.
The total sum is the sum of the numbers in both groups, which is:
Total sum = S1 + S2 = 600 + 1500 = 2100
The total count is the sum of the number of elements in both groups, which is:
Total count = 20 + 30 = 50
Therefore, the average of all the numbers in both groups is:
Average = Total sum / Total count = 2100 / 50 = 42
Therefore, the correct answer is: 42
Last updated on Jul 6, 2025
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