If you take 2 groups of equal cardinality, it could happen that, for example, many of the higher values go to the first group and therefore, many of the low values go to the second group, making their respective means quite different and different from the original sample mean. This could even go worse due to the possible existence of outliers, that is, values that are far different than the sample mean. An outlier tend to disrup the mean of a sample, but for smaller samples the result is much dramatic.
For example, let X be {1,2,3,4,5,6,7,8,9,100}
The elements of X sum 145, hence the mean of X is 14,5. Let divide X in two groups
Y = {1,2,3,5,9}
Z = {4,6,7,8,100}
The elements of Y sum 20, so its mean is 4
The elements of Z sum 125, so its mean is 25
Both means are quite different from each other and quite different from the mean of X. Note that if we take the mean of the means the result is 4+25/2 = 14,5 which is equal to the mean of X.
4. Let the numbers be x - 2, x, and x + 2, where x is an odd number.
2(x² - 4) - 4x = (x + 2)² + 21
2x² - 8 - 4x = x² + 4x + 4 + 21
2x² - 4x - 8 = x² + 4x + 25
x² - 8x - 33 = 0
(x - 11)(x + 3) = 0
x = 11, or -3
When x = 11, x - 2 = 9, x + 2 = 13
When x = -3, x - 2 = -5, x + 2 = -1
Explanation: You are on the right track. However, rather than having three unknown variables, try to reduce your working out to one unknown variable. Since you know they are consecutive odd numbers, you can simply let x be the middle term and the other two be + and - 2, provided x is an odd number.
That will reduce your variable issues, and helps as the first and third provide a difference of two squares, and this works out very nicely.
Q5: is essentially the same process. Let your variables be something in the form of one unknown variable, and you should be okay from there. Let me know if you're stuck.
They are similar AEB and BDC?
Keep note of these things before we start:
-Of is a keyword that tells us multiplication is being done
-x = total number of pages
-32% = 32/100 = .32
Okay, here we go:
32% of total number of pages = 80
.32 of x = 80
.32*x = 80
.32x = 80
.32x/.32 = 80/.32
x = 250
There are 250 pages in total in Katie's book.
To find out how many pages she has to read (y), subtract the pages read from the total:
TOTAL - PAGES READ = PAGES LEFT TO READ
250 - 80 = y
170 = y
Katie has 170 pages left to read
Hope this helps!
Answer:
x =(10-√112)/2=5-2√ 7 = -0.292
x =(10+√112)/2=5+2√ 7 = 10.292
