Why can't you avrage averages?

Answer 1

mathematically, you CAN take an average of averages.

But statistically, it won't be meaningful, because you will be combining information from non-identical studies.

Answer 2

Probably because you are working with weighted averages. You can average averages... but then you get just that, the average of the averages, and not an average of the whole system you are looking at. With weighted averages, some part going into the average counts more than another part.

For example say a restaurant serves the following number of tables on the given nights: M = 30, T = 28, W = 32, Th = 31, F = 29, Sat = 56, and Sun = 60

You can find the average # of tables served per day for the weeknights (M-F) and weekend nights (Sat & Sun):

Week nights: (30+28+32+31+29)/5 =30
Weekend nights: (56+60)/2=58

You might think if you were going to find the average for the whole entire week you could just average the average for week nights and weekend nights. That would give you (30+55)/2 which = 44.

However, when you look at the list of numbers originally provided, you can clearly see there are a lot more week nights than weekend nights (5 vs 2). When you average the 2 averages, you are saying that there are the same number of weekend nights as there are week nights when in reality we know that's not true.

Instead you have to determine the total number of tables for the entire week (30+28+32+31+29+56+60) and divide by the total number of days in the entire week (7). That gives you an average of 38 tables per day, which is smaller than the 44 we calculated by averaging the averages.

The number gets smaller because now you are taking into account that fewer tables are served during the week nights than on weekend nights and there are more week nights than weekend nights in the whole week.

Now, if you have the exact same number of terms going into your 2 averages, then the average of the averages will give you the right answer...

2 boys & 2 girls weigh themselves. Find the average of the boys, the average of the girls and the average of all 4 children if they weigh the following: Boy 1 = 56 lb, Boy 2 = 58 lb, Girl 1 = 40 lb, Girl 2 = 44 lb

Boys = (56+58)/2 = 57
Girls = (40+44)/2 = 42
Kids = (56+58+40+44)/4 = 49.5
Avg of Avg = (57+42)/2 = 49.5

But that's only because there are 2 boys & 2 girls so they are weighted equally when making up the average. It's safer to always work with totals when determining an average because then you will weight everything properly.

Answer 3

Under some circumstances you can, but the difficulty is that the individual averages might have to be weighted.

For instance, let's say eight people take a test. Their scores are 70, 74, 80, 82, 90, 90, 93, and 95.

The first six people have an average of 81, and the last two have an average of 94. You might be tempted to average the two averages to get a "class average" of 87.5, but if you actually average all the scores, you get 84.25. The discrepancy is caused by the fact that the two average numbers don't tell you how many data-points were used to determine them. Once you remember that three times as many data-points went into the first average as the second, you can weight them: ( 3*81 + 94 ) / 4 = 84.25.

Answer 4

You can take the average of the averages, but it totally depends on what kind of question you want answered. Taking average of the averages of groups is the same as combining all the groups and taking the average of the combined data if the groups are equally weighted. This idea is of importance in statistics and is used in a statistical model that was one of the first developed in statistics.

In terms of weighted average, this is not a problem if the weights are chosen to be some multiplicative constant of the sample size.

Answer 5

Because there is more than one type of average: the mean, median, or mode.
Let say you have a set of numbers: 2, 3, 4, 5, 6, 8, 8

The mean is when you take all the numbers and add them together and divide by the number of things.
(2+3+4+5+6+8+8)/6 =6

The median is just when you put all the number in order and pick the one in the middle:
2, 3, 4, *5*, 6, 8, 8 = 5

The mode is just the number listed the most
2,3,4,5,6,*8,8* = 8

You can take the mean of means or the mode of means or whatever, but you have to decide which "average" you want to use before you "average averages."

Answer 6

Well, we can. Say we have averages of, 6, 4, 5, 3, and 2; well the average of them is: 4. I know that was a rilddle but if it really was a maths question then do know that I passed my maths in College by 90%. Top of class by a clear 9%.

Good luck

Answer 7

You can. You just have to use some caution since it could give you misleading results if used inappropriately.

For example, no one has a constant body temperature. It changes over the course of the day and even over the course of the month. However, each person does have an average body temperature.

Each person's average body temperature is probably a little different than their neighbor's. However, you can average each person's average body temperature and expect to get a fairly accurate approximate average body temperature for humans. (It's about 36.8 degrees Celsius. For practical purposes, that's usually rounded off to about 37 degrees Celsius, which is usually converted to 98.6 degrees Fahrenheit in the US. Normally, you wouldn't keep more significant digits in your converted number than you started off with in the original number, but, ironically, 98.6 degrees winds up being a better number than the more accurate 98.2 degrees, since it reduces, ever so slightly, the number of new mothers hauling their child to the emergency room for a slight fever.)

On the other hand, if you averaged the IQ of students at the University of Michigan, at Ohio State University, UCLA, and at MIT, then averaged your averages, you might come to the conclusion that the average IQ is substantially higher than it really is. (Ohio St has 44,000 undergraduate students, UCLA and Michigan about 25,000, and MIT about 4,000).

Answer 8

You can average averages accurately if they are all equally weighted (ex. average GPA at a university is an average of averages of equal material).
You come into a problem when the averages you are averageing are not weighted equally (i.e. different amount of figures, different weights, etc.), because this gives you a skewed picture.
This won't work for your statistics class but most of the time in real life situations an average of an average will give you all the info you need as long as you don't need to be extremely precise.

Answer 9

An average is a single value based on the mean of several values. And you can find the average of 1 number.

However, if you have broken a large amount of data into several sets and each person calculates the average of 1 set. You can find the average of the averages from the different sets to find the actual average of the large amount of data.

Answer 10

with 3 different ways to create averages you would take those 3 averages and average them together in all 3 different ways and then have 3 averages of averages. So basically you can't average averages because there are too many ways to find averages. And if the averages are from different things you can't average them because they are not related.

Answer 11

well lets put it this way. if you find an average of height, average of weight, and average of how fast they run. what would be the point of taking those three averages and averaging them together? you're not going to find out new info on anything but get confused on the results. if an average was 66 inches 120lbs and the can run a mile about 8.5 minutes what kind of answer would you want when you averaged them together? jeeze this is really hard to explain check ya later ♥