46. Mean of n observations is š. If each of these observations is increased by 1, 2, 3, 4...n, respec-
tively, then what will be their mean?

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Explanation:

Consider the set

which has n items in it. We don't know anything about any individual item, but what we do know is that the mean is S.

So,

In short, the sum of the values is exactly nS, where S is the mean of the same set.

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Next, we add 1 to , add 2 onto , etc to form this new set

Let's find the mean like so

which is why S+0.5(n+1) is the answer

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Let's look at a concrete example.

Consider the set {1,7,10} which has n = 3 items in it.

Its mean is,

S = (1+7+10)/3 = 18/3 = 6

Now increase the items in {1,7,10} by adding on the values {1,2,3} to each element in the order shown

1+1 = 2

7+2 = 9

10+3 = 13

So {1,7,10} becomes {2,9,13}

The mean of the new set {2,9,13} is...

mean = (2+9+13)/3 = 24/3 = 8

Notice how,

newMean = S + 0.5(n+1)

newMean = 6 + 0.5(3+1)

newMean = 8

which helps us see how the formula works and partially confirm the answer. While this example isn't definitive proof, it's still handy to go over. I recommend forming other sets to check to see that this formula works. Not only do I recommend trying different values, but also a different number of values as well (i.e. increase n to some larger integer).

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.

the aswere is the one with all 8's and the second one is with the 10,8 and 6

step-by-step explanation: