Question

Find the interquartile range of the data set 43,36,51,68,50,27,38,81,33

Answer 1

The interquartile range (IQR) of the data set is the difference between the third quartile and the first quartile (Q3 - Q1). After arranging the data set in ascending order, Q1 is 34.5 and Q3 is 59.5, resulting in an IQR of 25.

Step-by-step explanation:

To find the interquartile range (IQR) of the provided data set (43,36,51,68,50,27,38,81,33), we first need to arrange the numbers in ascending order and then find the first quartile (Q1) and the third quartile (Q3). The IQR is the difference between Q3 and Q1.

1. Order the data set: 27, 33, 36, 38, 43, 50, 51, 68, 81
2. Find the median (which is also the second quartile or Q2): 43
3. The lower half of the data (before the median): 27, 33, 36, 38
4. The upper half of the data (after the median): 50, 51, 68, 81
5. Find Q1 (the median of the lower half): (33+36)/2 = 34.5
6. Find Q3 (the median of the upper half): (51+68)/2 = 59.5
7. Calculate the IQR: Q3 - Q1 = 59.5 - 34.5 = 25

Therefore, the IQR of the data set is 25.