I just need help getting the mean and Standard deviation of each sample Below are values from 4-6 randomly selected items from each of six different populations.Enter these into six different lists inyour calculator.Samples fromPopulation ASamples fromPopulation BSamples fromPopulation C42Samples fromPopulation XSamples fromPopulation YSamples fromPopulation Z6644918.295948407695425755346911624945822898565339462051Here is a dot plot of your sample data from A, B, and C:CСС с вс ВВ В В ВАА АA A102030405060708090100Does it appear that your samples from A, B, and C come from populations with differentmeans, or might populations A, B, and C have the same mean?Here is a dot plot of your sample data from X, Y, and Z:XY Z z YZZ XY XX XY Z102030405060708090100Does it appear that your samples from X, Y, and Z come from populations with differentmeans, or might populations X, Y, and Z have the same mean? Get the mean and standard deviation of each sample:STAT>CALC>1: 1-Var Statsa =Sa =Sx =ア=Sy =C =Sc =S, =Perform a 2-tailed, 2-Sample TTest to see if you can conclude u4 + µBPerform a 2-tailed, 2-Sample TTest to see if you can conclude µx # µyIIII

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Description: I just need help getting the mean and Standard deviation of each sample Below are values from 4-6 randomly selected items from each of six different populations.Enter these into six different lists inyour calculator.Samples fromPopulation ASamples f

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I just need help getting the mean and Standard deviation of each sample

Below are values from 4-6 randomly selected items from each of six different populations.
Enter these into six different lists in
your calculator.
Samples from
Population A
Samples from
Population B
Samples from
Population C
42
Samples from
Population X
Samples from
Population Y
Samples from
Population Z
66
44
91
8.
29
59
48
40
76
95
42
57
55
34
69
11
62
49
45
82
28
98
56
53
39
46
20
51
Here is a dot plot of your sample data from A, B, and C:
C
СС с вс ВВ В В ВАА А
A A
10
20
30
40
50
60
70
80
90
100
Does it appear that your samples from A, B, and C come from populations with different
means, or might populations A, B, and C have the same mean?
Here is a dot plot of your sample data from X, Y, and Z:
XY Z z YZ
Z X
Y X
X XY Z
10
20
30
40
50
60
70
80
90
100
Does it appear that your samples from X, Y, and Z come from populations with different
means, or might populations X, Y, and Z have the same mean?

Get the mean and standard deviation of each sample:
STAT>CALC>1: 1-Var Stats
a =
Sa =
Sx =
ア=
Sy =
C =
Sc =
S, =
Perform a 2-tailed, 2-Sample TTest to see if you can conclude u4 + µB
Perform a 2-tailed, 2-Sample TTest to see if you can conclude µx # µy
II
II

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution

Step 1

Values from 4-6 randomly selected items from each of six different populations are given as:

Sample from population A	Sample from population B	Sample from population C	Sample from population X	Sample from population Y	Sample from population Z
66	44	42	91	8	29
59	48	40	76	95	42
57	55	34	5	69	11
62	49	45	82	28	98
56	53	39	46		20
	51

Mean is sum of observations divided by number of observations, calculated as:

$x = \frac{\sum_{i = 1}^{n} x_{i}}{n}$

Standard deviation: The positive square root of mean of squares of the deviations taken from mean is known as standard deviation.

It is calculated as:

$s = \sqrt{\frac{\sum_{i = 1}^{n} {(x_{i} - x)}^{2}}{n - 1}}$

Step 2

Mean for the samples from population A is:

$\begin{array}{rcl} a & = & \frac{66 + 59 + 57 + 62 + 56}{5} \\ = & 60 \end{array}$

Standard deviation for the samples from population A is:

$\begin{array}{rcl} s_{a} & = & \sqrt{\frac{{(66 - 60)}^{2} + {(59 - 60)}^{2} + {(57 - 60)}^{2} + {(62 - 60)}^{2} + {(56 - 60)}^{2}}{5 - 1}} \\ = & 4.0620 \end{array}$

Mean for the samples from population Bis:

$\begin{array}{rcl} b & = & \frac{44 + 48 + 55 + 49 + 53 + 51}{6} \\ = & 50 \end{array}$

Standard deviation for the samples from population B is:

$\begin{array}{rcl} s_{b} & = & \sqrt{\frac{{(44 - 50)}^{2} + {(48 - 50)}^{2} + {(55 - 50)}^{2} + {(49 - 50)}^{2} + {(53 - 50)}^{2} + {(51 - 50)}^{2}}{6 - 1}} \\ = & 3.8987 \end{array}$

Mean for the samples from population C is:

$\begin{array}{rcl} c & = & \frac{42 + 40 + 34 + 45 + 39}{5} \\ = & 40 \end{array}$

Standard deviation for the samples from population C is:

$\begin{array}{rcl} s_{c} & = & \sqrt{\frac{{(42 - 40)}^{2} + {(40 - 40)}^{2} + {(34 - 40)}^{2} + {(45 - 40)}^{2} + {(39 - 40)}^{2}}{5 - 1}} \\ = & 4.0620 \end{array}$

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