Respuesta :
Answer:
The average of group A is 78.9 and average of group B is 82. Therefore group B has a higher average.
The standard deviation of A is 4.1 and standard deviation of B is 9.23, therefore group A is more consistent.
Step-by-step explanation:
The quiz scores for two different groups of math students are given below.
Group A – 75, 72, 77, 80, 87, 82, 79, 80, 75, 82
Group B – 71, 75, 85, 95, 71, 71, 90, 95, 87, 80
Formula for mean is
[tex]Mean=\frac{\sum x}{n}[/tex]
The average of group A is
[tex]Mean_A=\frac{75+72+77+80+87+82+79+80+75+82}{10}=\frac{789}{10}=78.9[/tex]
The average of group B is
[tex]Mean_B=\frac{71+75+85+95+71+71+90+95+87+80}{10}=\frac{820}{10}=82[/tex]
The average of group A is 78.9 and average of group B is 82. Therefore group B has a higher average.
Formula for standard deviation is
[tex]S.D.=\sqrt{\frac{\sum(x-\overline{x})^2}{n}}[/tex]
The standard deviation of group A is
[tex]S.D._A=\sqrt{\frac{168.9}{10}}\approx 4.1[/tex]
The standard deviation of group B is
[tex]S.D._B=\sqrt{\frac{852}{10}}\approx 9.23[/tex]
The standard deviation of A is 4.1 and standard deviation of B is 9.23, therefore group A is more consistent.
