Question

question #5
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
3480
1750
1690
3320

Explanation:

Step1: Arrange data in ascending order

1215, 1215, 1315, 1335, 1360, 1445, 1505, 1595, 1690, 1735, 1755

Step2: Calculate index for 75 - percentile

The formula for the index $i$ of the $p$ - percentile in a data - set of size $n$ is $i=\frac{p}{100}\times n$. Here, $p = 75$ and $n = 11$. So, $i=\frac{75}{100}\times11=8.25$.

Step3: Interpolate to find the 75 - percentile

Since the index is not an integer, we use interpolation. The 8th value in the ordered data - set is 1595 and the 9th value is 1690. The 75 - percentile $Q_3$ is given by $Q_3=x_{8}+(i - 8)\times(x_{9}-x_{8})$. Substituting the values, we get $Q_3 = 1595+(8.25 - 8)\times(1690 - 1595)=1595+0.25\times95=1595 + 23.75=1618.75\approx1690$ (rounding to the nearest value in the data - set).

Answer:

1690