Answer: The standard deviation of the sample will be 11.6.
The standard deviation of the population will be 12.31.
Step-by-step explanation:
Mr Smith's math class scores : 61, 67, 81, 83, 87, 88, 89, 90, 98, 100
Number of terms,N = 10
[tex]Mean=\mu =\frac{\text{sum of all the terms}}{\text{total number of terms}}[/tex]
[tex]\mu =\frac{61+67+81+83+87+88+89+90+98+100}{10}=\frac{844}{10}=84.4[/tex]
Standard deviation of the sample:
[tex]\sigma=\sqrt{\frac{1}{N}\sum_{i=1}^n(x_i-\mu )^2}=\sqrt{\frac{1}{10}(1364.4)}=11.68[/tex]
Standard deviation for the population:
[tex]\sigma=\sqrt{\frac{1}{N-1}\sum_{i=1}^n(x_i-\mu )^2}=\sqrt{\frac{1}{9}(1364.4)}=12.31[/tex]
The standard deviation of the sample will be 11.6.
The standard deviation of the population will be 12.31.
