Question

For the given set of numbers 2, 4, 13, 14, 19, 20, 27, the lower quartile, upper quartile, and interquartile range are:

(a) Lower quartile: 5, Upper quartile: 19, Interquartile range: 14

(b) Lower quartile: 6, Upper quartile: 20, Interquartile range: 14

(c) Lower quartile: 4, Upper quartile: 20, Interquartile range: 16

(d) Lower quartile: 4, Upper quartile: 19, Interquartile range: 15

Answer 1

The lower quartile is 4, the upper quartile is 19, and the interquartile range is 15.

Step-by-step explanation:

The given set of numbers is 2, 4, 13, 14, 19, 20, 27. To find the lower quartile, we divide the data into two halves. The lower half is 2, 4, 13 and the upper half is 14, 19, 20, 27.

The lower quartile (Q1) is the median of the lower half, which is 4. The upper quartile (Q3) is the median of the upper half, which is 19.

The interquartile range (IQR) is the difference between the upper quartile and the lower quartile, which is 19 - 4 = 15. Therefore, the correct answer is (d) Lower quartile: 4, Upper quartile: 19, Interquartile range: 15.