Question #350950

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

Expert's answer

**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;

- Find the median. This is the second quartile Q
_{2}. - At Q
_{2}split the ordered data set into two halves. - The lower quartile Q
_{1}is the median of the lower half of the data. - The upper quartile Q
_{3}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."

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