Greatest Standard Deviation????

Question

Which group of numbers has the greatest standard deviation?

a.) (1,2,3,4,5,6)

b.) (100,200,300,400,500,600)

c.) (100,100,100,600,600,600)

d.) (600,600,600,600,600,600)

Please EXPLAIN your answer. Thanks

Answer 1

the standard deviation is the simplest mathematical way to measure the statistical dispersion of any set of numbers. if the data points in a given set are close to the average of that set then the standard deviation will be small, if the data points are far from the average of that set then the standard deviation will be large.

to calculate the standard deviation, you must calculate the root mean square deviation of the values from their arithmetic mean (=average).

to calculate the average of the data set, add all the numbers in the set together then divide by the number of items in each set:

a) avg = (1+2+3+4+5+6)/6 = 3.5
b) avg = (100+200+300+400+500+600)/6 = 350
c) avg = (100+100+100+600+600+600)6 = 350
d) avg = (600+600+600+600+600+600)/6 = 600

given the defintion of standard deviation, (c) is the correct answer because its data points are on average farther from the arithmetic mean of the set compared to all the other answers. but let's go through the math of calculating the standard deviation.

since i can't use the proper mathematical notation, this may get somewhat hairy, but, hopefully it will be clear.

to calculate the standard deviation (=SD), you must:

1) calculate the difference between each point in the data set and the average
2) square the difference
3) sum all the differences
4) divide by the number of points in the data set (or the average of the sqared differences)
----this will give you the variance
5) take the square root of the variance
----this will give you the standard deviation

a) avg = 3.5
---1) 1-3.5= -2.5, 2-3.5=-1.5, 3-3.5=-0.5, 4-3.5= 0.5, 5-3.5= 1.5, 6-3.5=2.5
---2) (-2.5)(-2.5) = 6.25, (-1.5)(-1.5)= 2.25, (-0.5)(-0.5)= 0.25, (0.5)(0.5)= .25, (1.5)(1.5)= 2.25, (2.5)(2.5)= 6.25
---3) 6.25+2.25+.25+.25+2.25+6.25= 17.5
---4) 17.5/6= 2.9167 --this is the variance
---5) sqrt (2.91666)= 1.707 --this is the SD for answer (a)

b) avg = 350
---1) 100-350= -250, 200-350= -150, 300-350= -50, 400-350= 50, 500-350= 150, 600-350= 250
---2) (-250)(-250)= 62500, (-150)(-150)= 22500, (-50)(-50)= 2500, 50*50= 2500, 150*150= 22500, 250*250= 62500
---3) 62500*2+22500*2+2500*2= 175000
---4) 175000/6 = 29166.667 --this is the variance
---5) sqrt (29166.667)= 170.78 -this is is the SD for answer (b)

c) avg = 350
---1) 100-350= -250, 600-350= 250
---2) (-250)(-250) = (250)(250) = 62500
---3)&4) (62500 * 6)/6 = 62500
--this is the variance
---5) sqrt (62500)= 250 --this is the SD of answer (c)

d) avg = 600
---1) 600-600= 0
---2) 0*0=0
---3)&4)&5) (0*6)/6= 0.sqrt(0) = 0 --this is the SD of answer (d)

so, the answer, as we stated earlier is answer (c)

Answer 2

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It is possible for the standard deviation to be greater than the mean, even if all data points are positive numbers. However, the only way for this to happen is for most, if not all, data points to be at the extremes (with one extreme much greater in magnitude than the other) and nothing near the average. Generally, in a science experiment, it means the orignal data is garabage.

Answer 3

c) ....

the "mean-value) of C) is 350 and stdev is a measure of "distance from the mean"

If you go to EXCEL and type in the number
in a column each for a, b, c and d you get:
(at the bottom of each column type an "=" sign
and there's a little box in the upper left corner
taskbar with a "down-arrow" where you select
"STDEV" and the "wizard" will select the cells in the
column of values you've just typed and here are the results

[NOTE: "c" was the correct guess.]

good luck

a) 1.870828693
b) 187.0828693
c) 273.8612788
d) 0


STDEV = the square root of
...(1/(n-1) * the sum of
... ... (the 'value' - 'mean-value')^2 )

where "n" is the number of values under consideration
... ...

Answer 4

This Site Might Help You.

RE:
Greatest Standard Deviation????
Which group of numbers has the greatest standard deviation?

a.) (1,2,3,4,5,6)

b.) (100,200,300,400,500,600)

c.) (100,100,100,600,600,600)

d.) (600,600,600,600,600,600)

Please EXPLAIN your answer. Thanks

Answer 5

Ha, ha. Chanti picked the worst possible answer. Hey Chanti, forget about answering math questions and stick to questions about makeup.

Answer 6

C because the deviations from the mean are the largest

sd = sqrt(sum (xi - mean)^2)/n-21)

Answer 7

i would pick d) its standard,

not changing