Question

this data represents the number of cups of coffee sold in a cafe between 8 am and 10 am every day for 14 days.
{10,9,6,12,4,6,7,8,15,14,12,9,10,5}
the difference of the values of the first and third quartiles of the data set is?

Answer 1

To find the first quartile (Q1), we need to arrange the data set in increasing order:

{4, 5, 6, 6, 7, 8, 9, 9, 10, 10, 12, 12, 14, 15}

The position of the first quartile can be calculated as (14 + 1)/4 = 3.75. Since 3.75 is not a whole number, we take the average of the values at positions 3 and 4:

Q1 = (6 + 6)/2 = 6

To find the third quartile (Q3), we calculate the position as (14 + 1) * 3/4 = 10.5. Again, this is not a whole number, so we take the average of the values at positions 10 and 11:

Q3 = (10 + 10)/2 = 10

The difference between the first quartile (Q1) and the third quartile (Q3) is:

Q3 - Q1 = 10 - 6 = 4

Therefore, the difference of the values of the first and third quartiles of the data set is 4.