# How do I find the average of two averages?

• MHB
• Math_312 46
In summary, the average value of several measurements was 10.2 in a statistical study, while in a new survey, twice as many measurements were taken and their mean was 10.8. The sum of all 3n items is 31.7n and their mean is 10.6.
Math_312 46
In a statistical study, several measurements were taken and the average value of the measurements was 10.2. In a new survey, twice as many measurements were taken and the mean of these measurements was 10.8. What is the mean of all the measurements?

If the mean of "n" numbers is is 10.2 what is their sum?
If the mean of "2n" numbers is 10.8, what is their sum?

So what is the sum of all 3n items? What is theit mean?

Are you suggesting that I do this:
10.2 n / n = 10.2

or have I misunderstood you?

$\dfrac{10.2 \cdot n + 10.8 \cdot 2n}{n + 2n}$

skeeter said:
$\dfrac{10.2 \cdot n + 10.8 \cdot 2n}{n + 2n}$

So if I do this calculation, the answer is 21?

Math_312 46 said:
So if I do this calculation, the answer is 21?
no

skeeter said:
no

Is it then 7 or 15,9?

Math_312 46 said:
Is it then 7 or 15,9?

nosimplify the numerator
what does $(10.2)(n) + (10.8)(2n)$ equal?

simplify the denominator
what does $n+2n$ equal?

determine those two sums, then divide.

skeeter said:
nosimplify the numerator
what does $(10.2)(n) + (10.8)(2n)$ equal?

simplify the denominator
what does $n+2n$ equal?

determine those two sums, then divide.

Ah, I see now. So the answer is then 10,6?

Math_312 46 said:
Are you suggesting that I do this:
10.2 n / n = 10.2

or have I misunderstood you?

I said, in my first response was
Country Boy said:
If the mean of "n" numbers is is 10.2 what is their sum?
10.1n

If the mean of "2n" numbers is 10.8, what is their sum?
(10.8)(2n)= 21.6n

So what is the sum of all 3n items?[\quote]
10.1n+ 21.6n= 31.7n

What is their mean?
31.7n/(3n)= 31.7/3= 10.5666...

You have the wrong answer because n times 10.2 is 10.2n NOT 10.1n as you used.
2n times 10.8 is 21.6n as you have.

Altogether those add to 10.2n+ 21.6n= 31.8n.

The average of those 3n values is 31.8/3= 10.6.

## 1. What is the formula for finding the average of two averages?

The formula for finding the average of two averages is (average1 + average2) / 2. This means you add the two averages together and divide by 2.

## 2. Can I just add the two averages and divide by 2 to find the average of two averages?

No, you cannot simply add the two averages and divide by 2. This will not give you an accurate average of the two averages. You must use the formula (average1 + average2) / 2 to find the correct average.

## 3. How do I find the average of two averages if the number of values in each average is different?

If the number of values in each average is different, you will need to multiply each average by the number of values it represents, add them together, and then divide by the total number of values. For example, if average1 represents 3 values and average2 represents 5 values, the formula would be (average1 * 3 + average2 * 5) / (3 + 5).

## 4. Is it possible to find the average of more than two averages?

Yes, it is possible to find the average of more than two averages. You would use the same formula of (average1 + average2 + average3 + ...) / n, where n is the total number of averages you are averaging.

## 5. Can I use decimals or fractions when finding the average of two averages?

Yes, you can use decimals or fractions when finding the average of two averages. Just make sure to keep track of the decimal places and use the correct formula to find the accurate average.

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