Question: Seven samples were obtained having the values 21, 22, 26, 29, 27, 26 and 24

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Question: Seven samples were obtained having the values 21, 22, 26, 29, 27, 26 and 24. The mean and standard deviation values are ____________?

 

First: Find the Mean of the samples obtained:

1. Add the numbers to find their sum

21+22+26+29+27+26+24= 175

2. How many numbers where there.

n=7

3. Divide the sum of the numbers by the sample size 'n'

175 / 7 = 25

Therefore, the mean of these numbers is 25.

 

Second: Find the Standard Deviation:

The formula for standard deviation (SD) is

 

 

            where: ∑ means “sum of “

                                        x is the value in the data

                        μ is the mean of the data

                        N is the number of data points in the population

 

1. Find the Mean.

The mean of the data is given and solve above:

Μean (μ) = 25

2. For each data point, find the square of its distance to the mean.

 

 

 

 

(21-25) ^2 = 16

(22-25) ^2 = 9

(26-25) ^2 = 1

(29-25) ^2 = 16

(27-25) ^2 = 4

(26-25) ^2 = 1

(24-25) ^2 = 1

 

3. Sum the values from Step b.

 

16+9+1+16+4+1+1 = 48

 

4. Divide by the number of data points.

 

 

 

N=7

 

48 / 7 = 68.85714

 

5. Take the square root.

SD = √68.85714

SD = 2.61861

 

Therefore, the standard deviation is 2.61861.