Question

Take the mean (average) and sample standard deviation of the sixteen numbers below.

25.25881	25.27368	25.21009	25.2202
25.2925	25.20889	25.22643	25.21332
25.24447	25.21286	25.24233	25.25303
25.27901	25.2939	25.23751	25.20013

Mean:

Standard Deviation:

% Relative Standard Deviation (aka CV):

95% Confidence interval (tcrit = 2.086 at 95% CL, 20 DoF):

Next take the mean of each set of four numbers (columns) and then take the mean and standard deviation of the four numbers that are the means of the sets of four.

Mean:

Standard Deviation:

Can the mean be different from the one above?

Why is the standard deviation different? (There is a special name for this, if you remember it.)

Answer 1

• Mean:
  
• Standard Deviation:
  
• C.V:
  
• To obtain the CI, First we've to assume that the data is following Normal Distribution.
  and here we obtaion the CI for Population Mean.
  
  
• We've to calculate the mean of each set of four numbers (columns) and then take the mean and standard deviation of the four numbers that are the means of the sets of four.
  

1. The first set-

   25.25881

   25.2925

   25.24447

   25.27901

• Mean:
  
• Standard Deviation:
  
• 2.The second set-

  25.27368

  25.20889

  25.21286

  25.2939

• Mean:
  
• Standard Deviation:
  
• 3. The third set-

  25.21009

  25.22643

  25.24233

  25.23751

• Mean:
  
• Standard Deviation:
  
  
• 4. The fourth set-

  25.2202

  25.21332

  25.25303

  25.20013

• Mean:
  
• Standard Deviation:
  
  
  GRAND MEAN
  
  
  STANDARD DEVIATION OF THE FOUR MEANS=0.020983
• No, the mean can't be different from the above.
• The Standard Deviation is called Standar Error.

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