What are the value of scores?

Question

A box and whisker plot is given. The description "test results of seven students" is given for the plot.

The following data is show in the box and whisker plot:

Minimum value - 1

Maximum value - 10

Lower quartile - 3

Upper quartile - 6

Median - 5

 

The mean is also given: 5

Only two students scored the same result. The rest of the scores are integral values.

Find the value of scores of the seven students. Show reasoning. 

For a test:)

Answer 1

the max and min will give you two students score, so it were 1 and 10

 

since there is seven students, then the median will be 5 due to odd students, and no need to do the average for median (only even numbers will use the average formula)

 

the lower and upper quartile are split in half by the median = 5 and then find the median again from the half of the data. This means the lower and upper quartiles will have three students scores. (again, it's odd number)

 

lower = 3  and upper = 6

 

 

now have two left that needs to figure out. the average comes in to figure that out.  Average is 5 and the total score of the seven students will be 5*7 = 35

 

let say X and Y are the two unknown left

seven students order

1 , 3 , X , 5 , Y , 6 , 10

 

add 1+3+5+6+10 + X +Y= 35

 

25 +X +Y = 35

 

X+Y = 10

 

now, here are the options for X and Y ( two possible solutions)

 

5 + 5 = 10 wont work since there will be three 5

 

4+6 = 10  works since 6 will be the double

 

3+7 = 10  wont work sinc 7 will change the upper quartiles

 

2 +8 = 10  wont work since 2 and 8 will change the lower and upper quartiles

 

 

solution

 

1 , 3 , 4 , 5 , 6 , 6 , 10