Beth and Amy are trading marbles. Beth has three times more marbles than her sister, Amy.
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Answer:
(1) Variance = 4.5 and Standard deviation = 2.121.
(2) Variance = 4.5 and Standard deviation = 2.121.
(3) The effect on the measure of dispersion if each value is changed uniformly is that it remains unchanged.
Step-by-step explanation:
We are given with the following set of data below;
X
5 5 - 8 = -3 9
5 5 - 8 = -3 9
8 8 - 8 = 0 0
10 10 - 8 = 2 4
10 10 - 8 = 2 4
10 10 - 8 = 2 4
9 9 - 8 = 1 1
9 9 - 8 = 1 1
<u> 6 </u> 6 - 8 = -2 <u> 4 </u>
Total <u> 72 </u> <u> 36 </u>
<u>Firstly, the mean of the above data is given by;</u>
Mean, =
= = 8
(1)Now, the variance of the given data is;
Variance =
= = 4.5
So, the standard deviation, (S.D.) =
= = 2.12
(2) Now, each value is added by 2; so the new data set is given by;
X
7 7 - 10 = -3 9
7 7 - 10 = -3 9
10 10 - 10 = 0 0
12 12 - 10 = 2 4
12 12 - 10 = 2 4
12 12 - 10 = 2 4
11 11 - 10 = 1 1
11 11 - 10 = 1 1
<u> 8 </u> 8 - 10 = -2 <u> 4 </u>
Total <u> 90 </u> <u> 36 </u>
<u>Firstly, the mean of the above data is given by;</u>
Mean, =
= = 10
(1)Now, the variance of the given data is;
Variance =
= = 4.5
So, the new standard deviation, (S.D.) =
= = 2.12
(3) The effect on the measure of dispersion if each value is changed uniformly is that it remains unchanged as we see in the case of variance or standard deviation.
Answer:
The second function represents an even function;
Step-by-step explanation:
A function f(x) is said to be even if f(x) = f(-x). All we need to do is replace x with -x in each equation, simplify it and assess whether the equation remains unchanged. If the equation is identical to the original one then it is said to be even. Another good example of an even function is the cosine function. Moreover, even functions have y-axis symmetry