This data set represents the number of cups of coffee sold in a café between 8 a. m. and 10 a. m. 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

The difference of the values of the first and third quartiles of the data set is 6.

Step-by-step explanation:

Data : 10, 9, 6, 12, 4, 6, 7, 8, 15, 14, 12, 9, 10, 5

This data set represents the number of cups of coffee sold in a café between 8 a.m. and 10 a.m. every day for 14 days.

Arrange the data in the ascending order :

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

No. of observations n = 14(even)

Median =

So, Median =

Median =

Median =

Median =

Median = 9

Now to find  i.e. Third quartile

Consider the set of values right to the median .

9,10,10,12,12,14,15

Now find the median of this data

No. of observations n = 7(odd)

So, Median =

=  

=

=

=

So,  

Now to find  i.e. First quartile

Consider the set of values left to the median .

4,5,6,6,7,8,9

No. of observations n = 7(odd)

So, Median =

=  

=

=

=

So,  

Now The difference of the values of the first and third quartiles of the data set  : 12-6=6

Hence The difference of the values of the first and third quartiles of the data set is 6

d. it is a convex pentagon because it has five sides and none of the sides would extend into the inside of the polygon.

step-by-step explanation: