Answer:
The interquartile range is 5
Step-by-step explanation:
The interquartile range is the third quartile less the first quartile. Therefore, we need to organize the data from the smallest to the largest as:
11, 12, 14, 14, 16, 16.5, 18, 18, 20
Additionally, to find the position of the quartil i we can use the following equation:
Position Qi = i * (n+1)/4
Where n is the size of the data and i can be 1, 2 or 3.
So, if we replace n by 9 and i by 1, we get:
Position Q1 = 1 * (9+1)/4 = 2.5
it means that the first quartile is between the numbers on position 2 and 3 and we can calculated that quartile as:
Q1 = (Value 2nd position + Value 3rd position)/2 = (12+14)/2 = 13
At the same way, the position of the third quartile is calculated as:
Position Q3 = 3 * (9+1)/4 = 7.5
it means that the third quartile is between numbers on position 7 and 8 and we can calculated that quartile as:
Q3 = (Value 7th position + Value 8th position)/2 = (18+18)/2 = 18
Finally, the IQR is:
Q3 - Q1 = 18 - 13 = 5
