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?
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.