Answer:
Quartile 1 (Q1) = 24
Quartile 2 (Q2) = 47
IQR = 23
Step-by-step explanation:
Given:
The set of data are:
13, 23, 24, 25, 26, 26, 37, 47, 47, 48, 50
The data are in increasing order. The number terms are, [tex]n = 11[/tex].
Therefore, the middle term = [tex]\frac{n+1}{2}=\frac{11+1}{2}=6^{th}\ term[/tex]
So, the median = 26
Now, the median divides the set of data into two parts. The median of first part is the quartile 1 and the median of second part is quartile 2.
So, the first part has the following terms:
13, 23, 24, 25, 26
Here also, [tex]n=5[/tex]. So, the third term is the median.
∴ Q1 = 24
The second part has the following terms:
37, 47, 47, 48, 50
Here also, [tex]n=5[/tex]. So, the third term is the median.
∴ Q2 = 47.
Now, IQR = Q2 - Q1 = 47 - 24 = 23.
