Answer to Question #350950 in Statistics and Probability for sergu

Question

The number of traffic violation recorded by police department for 10 day period is given. Calculate the first quartile, second quartile, third quartile and inter quartile range.

22 19 25 24 18 15 9 12 16 20

Answer 1

Solution:

To find quartiles, we nee to order data set from lowest to highest values:

22 19 25 24 18 15 9 12 16 20

1-9;

2-12;

3-15;

4-16;

5-18;

6-19;

7-20;

8-22;

9-24;

10-25;

1. Find the median. This is the second quartile Q₂.
2. At Q₂ split the ordered data set into two halves.
3. The lower quartile Q₁ is the median of the lower half of the data.
4. The upper quartile Q₃ is the median of the upper half of the data.

The median $\frac{(n+1)}{2}=\frac{10+1}{2}=5.5;$ it means, between 5 and 6 order: 18.5;

$Q_2=18.5;$ So, $Q_1=15;$ $Q_3=22;$

The Inter quartile range: $IQR=Q_3-Q1=22-15=7;$

Answer:

$Q_1=15;$

$Q_2=18.5;$

$Q_3=22;$

$IQR=7.$