please help with standard deviation?

Question

1.Find the mean and the standard deviation of this set of data.
24, 25, 15, 19, 17
2. Make up a set of five data items that has the same mean as the data set in question 1 but has a smaller standard deviation
3. Make up a set of five data items that has the same mean as the data set in Question 1 but has a larger standard deviation
4.Make up a set of data items that has the same standard deviation as the data set in question 1 but has a different mean.

Answer 1

Mean (x`) = (x1+x2+x3+x4+x5)/5
Standard Deviation (SD) = √[ (Σ|x - x`|²) / n]
(1)
x` = [24 + 25 + 15 + 19 + 17]/5
x` = 100/5
x` = 20

SD = √[ (Σ|x - x`|²) / n]
SD = √[ |24 - 20|² + |25 - 20|² + |15 - 20|² + |19 - 20|² + |17 - 20|² / 5]
SD = √[ |4|² + |5|² + |5|² + |1|² + |3|² / 5]
SD = √[ 16 + 25 + 25 + 1 + 9 / 5]
SD = √[ 76 / 5]
SD = √[ 15∙2 ]
SD = 3∙898717738

(2)
The range of numbers in question one: 17 → 25.
Shorten this range of numbers to give the same average. Since the mean is 20, you can arrange the numbers around 20. Then check the standard deviation value.
18, 19, 20, 21, 22.
x` = 20.
SD = 1∙414213562

(3)
For a larger deviation, have a bigger range or numbers. Then check the standard deviation value.
14, 17, 20, 23, 26.
x` = 20.
SD = 4∙242640687

(4)
For all the given data points, increase or decrease the values by the same amount.
22 + 23 + 13 + 17 + 15
X` = 18.
SD = 3∙898717738

Answer 2

So you need help with homework?
Mean is the average of your items.
Standard deviation means how far off the items are from the mean.
You need to understand that first.

Now, I'm not gonna do your homework, but I'll give you one example close to that.
The dataset 25, 50, 75 has the mean 50 and the standard deviation 25.
The dataset 40, 50, 60 has the same mean, 50, but standard deviation is only 10.
The dataset 50, 75, 100 has the mean 75 but the same standard deviaton like the first one: 25.

Your greatest help with this is Microsoft Excel. The function for mean is AVERAGE() and for standard deviation is STDEV(). If you can't use the formulas from the class to get your problem solved, experiment with numbers in Excel until you find a solution.

Answer 3

1) the mean is 20, and the standard deviation is 3.89
just plug into calculator

2) 18, 19, 20, 21, 22, standard deviation is 1.41
make your spread tighter

3) 10, 15, 20, 25, 30 standard deviation is 7.07
make your spread broader

4) 23, 24, 14, 18, 16, mean is 19
bring each number down my one

Answer 4

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Answer 5

1. mean i.e average is m=(24+25+15+19+17)/5=100/5=20
standard deviation d=(1/N*summation(Xi-m)^2)^1/2, i=1,2,3,4,5
X1=24, X2=25,X3=15,X4=19,X5=17
N=no of numbers=5, putting the values of Xi we get
d=(((24-20)^2+(25-20)^2+(20-15)^2+(20-19)^2+(20-17)^2)/5)^1/2
=3.9
2. set is 18,19,20,21,22 ; m=20 ; d=1.414
3. set is 12,16,20,24,28 ; m=20 ; d=5.657
4. set is 14,15,20,22,24 ; m=19 ; d= 3.9

Answer 6

Someone's having a tough time with their statistics homework. Probably should have stayed awake in class.

Answer 7

mean 20.76, sd 4.359