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How do you calculate an overall average from a set of component averages?
Wiki User
∙ 14y ago
I recommend you do not try to average a set of components, because your result may be not be accurate. The best way to find an overall average is to average the entire data set.
EXAMPLE: You have three columns of ten numbers each with an average listed at the bottom of each, say A11, B11, and C11. There are two ways you can solve this:
- Combine all the averages and divide by 3. [=SUM(A11:C11)/3] - But, the result may not reflect the average of the entire data set.
- Calbulate the average for all 30 numbers in the data set. [=SUM(A1:C10)/30] - This would give a much more accurate representation of the entire data set.
Wiki User
∙ 14y ago
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Is an average of a set of numbers the same as the average of the averages of the subsets of numbers?
No, it is not. Example: the average of (5 and 7) is 6, and the average of (50, 60 and 70) is 60, but if we add all five numbers we have 192, so the overall average is 192 divided by 5 = 38.4 and the reason for that is we have more and bigger numbers in the second set.
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Overall classification, control markings(if applies), Component, office of origin and date, page and portion markings, classified by, downgrade to (if applies), derived from and declassify on lines
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which component of brading does ''moving forward'' in the overall standard bank brand represent?
Is an average of a set of numbers the same as the average of the averages of the subsets of numbers?
No, it is not. Example: the average of (5 and 7) is 6, and the average of (50, 60 and 70) is 60, but if we add all five numbers we have 192, so the overall average is 192 divided by 5 = 38.4 and the reason for that is we have more and bigger numbers in the second set.
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Is an average of averages accurate?
Mx = MM is the greek letter mu, by the way.Statistically speaking, an average of averages within a sample is said to very closely approximate the population average. However, where the sample size is under 30, there needs to be an adjustment for size. If the sample is over 30 (thus you are averaging over 30 averages), then this should reflect very closely the population average. It is not perfect but statistically it is incredibly close.However, it is important not to compare apples and oranges in general so while giving mu of mu, be sure to include the standard deviation and any notes you find relevant.Average of averagesYou're living dangerously.If the averages don't have equal weight, your average of averages will yield skewed results. Here's why.Let's say you're trying to calculate your overall average grade for all the tests you've taken in school, and let's say you are taking only math, English, and science. Let's say your average in math is 80, English is 85, and science is 90. The average of those averages is, of course, 85. But is that your true average?Not if you took ten math tests, five English tests, and only two science tests!! If all those tests have equal value, then your average is closer to 80, because the ten math tests dominate the true average. In other words, your true average is the WEIGHTED average of the three averages. To weight them properly, you must think of the math average as not one data point but ten data points, the English average as not one data point but five, and the science average as not one but two data points.Here's how the weighted average math looks:10 x 80 = 8005 x 85 = 4252 x 90 = 180__ ___17 1405Now, divide 1405 by 17. So, 1405/17 = 82.7. (The 17 is the sum of the weighting factors, which, as you can see, is equal to the total number of tests you took.)So, you can see that taking the average of averages may give erroneous results -- unless you find the weighted average.
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Average daytime high temperatures go from 7 (45) in January to 22 (72) in July.Nightime lows go from 2 (36) to 13 (57).Monthly averages go from 5 (41) to 18 (64).The overall yearly average is a minimum 8 (46) and maximum 14 (58) with an overall average of 11 (52).All figures are Celsius (Fahrenheit in parentheses).See the Related Link
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