Answer to Question #142946 in Statistics and Probability for Margaret

Question

For sample of 11 units production employee during the most recent days
30 16 17 18 15 19 21 25 31 33 41
Which one of the following statement is incorrect?
1. The position of Q1=3
2. The value of Q2 =19
3. The media is 21
4. The value of Q3 is 31
5. The interquartile range is 14

Answer 1

Solution

First arrange the data in ascending order:

15 16 17 18 19 21 25 30 31 33 41

$Q_1$ is the $({n+1 \over 4}) ^{th}$ term i.e

$$({ 11+1 \over 4})= 3^{rd} \space term =17$$

$Q_2 = median$ is the $({n+1 \over 2})^{th}$ term i.e

$${11+1 \over 2}= 6^{th} \space term = 21$$

$Q_3$ is the ${{3 \over 4}{( n+1)}}^{th}$ term i.e

$${3 \over 4}{(11+1)} = 9^{th} \space term = 31$$

Imterquartile range:

$$Q_3 - Q_1 = 31 - 17 = 14$$

$\therefore$ the incorrect statement is that the value of $Q_2 =19$