Question

The quiz scores for two different groups of math students are given below. Use the mean and standard deviation to determine which group has a higher average, and which group is more consistent. Group A – 75, 72, 77, 80, 87, 82, 79, 80, 75, 82 Group B – 71, 75, 85, 95, 71, 71, 90, 95, 87, 80

Answer 1

Group b would probably have the higher average

Answer 2

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

$Mean=\frac{\sum x}{n}$

The average of group A is

$Mean_A=\frac{75+72+77+80+87+82+79+80+75+82}{10}=\frac{789}{10}=78.9$

The average of group B is

$Mean_B=\frac{71+75+85+95+71+71+90+95+87+80}{10}=\frac{820}{10}=82$

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

$S.D.=\sqrt{\frac{\sum(x-\overline{x})^2}{n}}$

The standard deviation of group A is

$S.D._A=\sqrt{\frac{168.9}{10}}\approx 4.1$

The standard deviation of group B is

$S.D._B=\sqrt{\frac{852}{10}}\approx 9.23$

The standard deviation of A is 4.1 and standard deviation of B is 9.23, therefore group A is more consistent.