To answer this question, we need to find the following statistics (because we have a box plot in the question): minimum value, first quartile, median (second quartile), third quartile, and, finally, the maximum value for this list of numbers.
To find that, we need to order the list from the minimum value to the maximum value in ascendent order:
From the list of 10 numbers: 5, 9, 11, 6, 5, 8, 11, 3, 12, 6, we have (in ascendent order):
l = {3, 5, 5, 6, 6, 8, 9, 11, 11, 12}
Now, we can identify
• The minimum number is equal to 3.
,
• The maximum number is equal to 12.
We need to find the median or the value for which the 50% of the values are less or greater than this number. To find it, we have ten ordered numbers:
3, 5, 5, 6, 6, 8, 9, 11, 11, 12
Since we have an even number of numbers here, we need to take the two central values and then take their mean:
[tex]m=\frac{6+8}{2}=\frac{14}{2}\Rightarrow m=7[/tex]
Then, the value for the median is 7.
Now, we need to find the First Quartile. To do this, we need to take the first half of the numbers and do a similar process as we did with the median to obtain the first quartile, that is, a number where 25% of the numbers are less than it, and 75% are greater than this number. Then, we have:
3, 5, 5, 6, 6
And we see that this number is equal to 5. Then, the first quartile is equal to 5.
We will repeat the same procedure to find the third quartile:
8, 9, 11, 11, 12
Therefore, the third quartile is equal to 11.
In summary, we have that the numbers must be placed as follows:
3 5 7 11 12 (answer)
