1. Calculate standard deviatio
1. Calculate standard deviation forthe following population of N = 6 scores: 5, 0, 9, 3, 8,5. Use the computational formula and show your work.(Hint: You should get the same answer for this questionthat you got for question #2).
For the following sample, use the computational formula tocalculate SS and then compute the sample variance andstandard deviation. Scores: 1, 4, 2, 1
A distribution of scores has a mean of M = 42. If thestandard deviation is SD = 2, would a score of X= 48 be considered an extreme value?
Answer:
1) For the given sample 5, 0, 9, 3, 8, 5. to find the populationstandard deviation we need to find the mean first as:
Mean = (5 + 0 + 9 + 3 + 8 + 5)/6= 30/6Mean = 5
The standard deviation for mean is calculated as:
σ =√(1/6 ) x ((5 – 5)2 + ( 0 – 5)2 + ( 9 -5)2 + ( 3 – 5)2 + ( 8 – 5)2 + ( 5- 5)2)= √(1/6) x ((0)2 + (-5)2 + (4)2 +(-2)2 + (3)2 + (0)2)= √(1/6) x ((0) + (25) + (16) + (4) + (9) + (0))= √(1/6) x (54)= √(9)= 3
2) The SS ( Sum of squares) for the values 1, 4, 2, 1 iscalculated as:
SS=(12+42+22+12)-(82)/4
Where Xi is the values and N is no of values which is 4.
SS=6
Sample variance is calculated as:
=> S2= SS/N-1
=> 6/(4-1)
=>2
Standard deviation=√S2
Sd= √2
=> 1.414
c) The given distribution of scores has a mean of M =42. If the standard deviation is SD = 2, to find a scoreof X = 48 is an extreme or typical we need to find the Zscore which is calculated as:
any score which is having Z score more than 3 or less -3 thatvalue is an extreme value hence the value X=48 is an extremevalue.
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