what is the interquartile range of this data set 1,5,27,29,34,37,48,61,72,84,96\na. 64\nb. 10\nc. 37\nd. 45
what is the interquartile range of this data set 1,5,27,29,34,37,48,61,72,84,96\na. 64\nb. 10\nc. 37\nd. 45
Answer
Explanation:
Step1: Arrange data in order
The data set is already in ascending - order: 1, 5, 27, 29, 34, 37, 48, 61, 72, 84, 96.
Step2: Find the median (Q2)
There are (n = 11) data points. The median is the (\left(\frac{n + 1}{2}\right))-th value. (\frac{11+1}{2}=6) - th value. So, (Q2=37).
Step3: Find the lower half and Q1
The lower half of the data is 1, 5, 27, 29, 34. There are (n_1 = 5) data points. The median of the lower - half ((Q1)) is the (\left(\frac{5 + 1}{2}\right))-th value, which is the 3 - rd value. So, (Q1 = 27).
Step4: Find the upper half and Q3
The upper half of the data is 48, 61, 72, 84, 96. There are (n_2 = 5) data points. The median of the upper - half ((Q3)) is the (\left(\frac{5+1}{2}\right))-th value, which is the 3 - rd value. So, (Q3 = 72).
Step5: Calculate the inter - quartile range (IQR)
The inter - quartile range is (IQR=Q3 - Q1). Substitute (Q1 = 27) and (Q3 = 72) into the formula: (IQR=72−27 = 45).
Answer:
D. 45