Question

question #5
find the lower quartile of the following set of data:
2550 2670 2750 2990 3200
3305 3350 3645 3690 3690
1525
1220
1440
2750
question #6
the weights of the top 11 best - selling cars at a dealership are listed below. find the weight of the car that separates the lowest 75% of weights from the highest 25% of weights.
car masses (kg)
1215 1595 1690 1755 1215
1360 1445 1505 1335 1735
1315
1690
1750
3320
3480

Explanation:

Step1: Sort the data

For Question #5, the data is already sorted. For Question #6, sort the data: \(1215,1215,1315,1335,1360,1445,1505,1595,1690,1735,1755\)

Step2: Find the position of the quartile

The formula for the position of the lower quartile (\(Q_1\)) is \(i=\frac{n + 1}{4}\), where \(n\) is the number of data points.
For Question #5, \(n = 11\), \(i=\frac{11+ 1}{4}=3\). The 3rd - value in the sorted data \(2550,2670,2750,2990,3200,3305,3350,3645,3690,3690\) is \(2750\)
For Question #6, \(n = 11\), the formula for the position of the upper quartile (\(Q_3\)) (which separates the lowest \(75\%\) from the highest \(25\%\)) is \(i=\frac{3(n + 1)}{4}\). \(i=\frac{3\times(11 + 1)}{4}=9\). The 9th - value in the sorted data \(1215,1215,1315,1335,1360,1445,1505,1595,1690,1735,1755\) is \(1690\)

Answer:

Question #5: \(2750\)
Question #6: \(1690\)