Question

Please follow the above definitions in calculating the quartiles. There are two distinct situations: set size equal to a power of 4 (L is already a whole number – integer), set size not a power of 4.

Note: each of the following problems is 15 points.

PROBLEM 2: Average wait in minutes for the train QM3; n=12

15 4 5 9 6 12 17 10 8 13 8 16

PROBLEM 3: Quiz scores L n = 13 students

5   7   9   10   8   9   0   6   7   10   9   10   8

PROBLEM 4: Grades received in BUS310-01 course:

66        53        89        92        98        72        71        80       

PROBLEM 5: Time to do a specific job (in minutes)

33        42        62        25        35        45        80        40        30        25

PROBLEM 6: Time to complete the exam

33        42        62        25        35        45        60        40        30        25            60

Answer 1

2.

In increasing order we have as follows.

4,5,6,8,8,9,10,12,13,15,16,17

Number of observations = 12

So, second quantile (median) is average of 12/2=6th and 12/2+1=7th observations.

First quantile is average of 3rd and 4th observations.

Third quantile is average of 9th and 10th observations.

So, first, second and third quantiles are 7,9.5 and 14 respectively.

3.

In increasing order we have as follows.

0,5,6,7,7,8,8,9,9,9,10,10,10

Number of observations = 13

So, second quantile (median) is (13+1)/2=7th observations.

First quantile is average of 3rd and 4th observations.

Third quantile is average of 10th and 11th observations.

So, first, second and third quantiles are 7.5, 8 and 9.5 respectively.

4.

In increasing order we have as follows.

53,66,71,72,80,89,92,98

Number of observations = 8

So, second quantile (median) is average of 8/2=4th and 8/2+1=5th observations.

First quantile is average of 2nd and 3th observations.

Third quantile is average of 6th and 7th observations.

So, first, second and third quantiles are 68.5, 76 and 90.5 respectively.

5.

In increasing order we have as follows.

25,25,30,33,35,40,42,45,62,80

Number of observations = 10

So, second quantile (median) is average of 10/2=5th and 10/2+1=6th observations.

First quantile is the 3rd observations.

Third quantile is the 8th observations.

So, first, second and third quantiles are 30, 37.5 and 45 respectively.

6.

In increasing order we have as follows.

25,25,30,33,35,40,42,45,60,60,62

Number of observations = 11

So, second quantile (median) is the (11+1)/2=6th observations.

First quantile is the 3rd observations.

Third quantile is the 9th observations.

So, first, second and third quantiles are 30,40 and 60 respectively.