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

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.

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=(\sum x)/(n)`

The average of group A is

`Mean_A=(75+72+77+80+87+82+79+80+75+82)/(10)=(789)/(10)=78.9`

The average of group B is

`Mean_B=(71+75+85+95+71+71+90+95+87+80)/(10)=(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{(168.9)/(10)}\approx 4.1`

The standard deviation of group B is

`S.D._B=\sqrt{(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.