a basketball player recorded her points for 11 consecutive games. her points are listed below. 13, 20, 15…

a basketball player recorded her points for 11 consecutive games. her points are listed below. 13, 20, 15, 22, 24, 21, 18, 20, 25, 17, 27 how many points would she need to score in her 12th game in order to decrease the interquartile range by 1 point?\n13\n15\n23\n25

a basketball player recorded her points for 11 consecutive games. her points are listed below. 13, 20, 15, 22, 24, 21, 18, 20, 25, 17, 27 how many points would she need to score in her 12th game in order to decrease the interquartile range by 1 point?\n13\n15\n23\n25

Answer

Answer:

15

Explanation:

Step1: Arrange data in ascending order

13, 15, 17, 18, 20, 20, 21, 22, 24, 25, 27

Step2: Find quartiles for 11 - game data

The median (Q2) of 11 - data points is the 6th value, Q2 = 20. The lower half is 13, 15, 17, 18, 20. The median of lower half (Q1) is 17. The upper half is 21, 22, 24, 25, 27. The median of upper half (Q3) is 24. The inter - quartile range (IQR) = Q3 - Q1 = 24 - 17 = 7.

Step3: Test each option

If we add 13: New data set in order: 13, 13, 15, 17, 18, 20, 20, 21, 22, 24, 25, 27. Q1 = 15, Q3 = 22.5, IQR=22.5 - 15 = 7.5. If we add 15: New data set in order: 13, 15, 15, 17, 18, 20, 20, 21, 22, 24, 25, 27. Q1 = 15, Q3 = 22, IQR = 22 - 15 = 7 - 1=6. If we add 23: New data set in order: 13, 15, 17, 18, 20, 20, 21, 22, 23, 24, 25, 27. Q1 = 17.5, Q3 = 23.5, IQR = 23.5 - 17.5 = 6, but we want to decrease by exactly 1 point and this is a different way of getting 6. If we add 25: New data set in order: 13, 15, 17, 18, 20, 20, 21, 22, 24, 25, 25, 27. Q1 = 17.5, Q3 = 24.5, IQR = 24.5 - 17.5 = 7. So the answer is 15.