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? 13 15 23 25
Answer
Answer:
15
Explanation:
Step1: Arrange data in ascending order
13, 15, 17, 18, 20, 20, 21, 21, 22, 24, 25, 27
Step2: Find Q1 and Q3 for original data
There are $n = 11$ data - points. The position of Q1 is $\frac{n + 1}{4}=\frac{11+1}{4}=3$rd value, so Q1 = 17. The position of Q3 is $\frac{3(n + 1)}{4}=\frac{3\times(11 + 1)}{4}=9$th value, so Q3 = 22. The original IQR=Q3 - Q1=22 - 17 = 5.
Step3: Test each option
Option A: If new value is 13
New data set in ascending order: 13, 13, 15, 17, 18, 20, 20, 21, 21, 22, 24, 25, 27. $n = 12$. Position of Q1 is $\frac{n}{4}=3$rd value, Q1 = 15. Position of Q3 is $\frac{3n}{4}=9$th value, Q3 = 21. IQR=21 - 15 = 6.
Option B: If new value is 15
New data set in ascending order: 13, 15, 15, 17, 18, 20, 20, 21, 21, 22, 24, 25, 27. $n = 12$. Position of Q1 is $\frac{n}{4}=3$rd value, Q1 = 15. Position of Q3 is $\frac{3n}{4}=9$th value, Q3 = 21. IQR=21 - 15 = 6, and original IQR was 5, so it decreases by 1.
Option C: If new value is 23
New data set in ascending order: 13, 15, 17, 18, 20, 20, 21, 21, 22, 23, 24, 25, 27. $n = 12$. Position of Q1 is $\frac{n}{4}=3$rd value, Q1 = 17. Position of Q3 is $\frac{3n}{4}=9$th value, Q3 = 23. IQR=23 - 17 = 6.
Option D: If new value is 25
New data set in ascending order: 13, 15, 17, 18, 20, 20, 21, 21, 22, 24, 25, 25, 27. $n = 12$. Position of Q1 is $\frac{n}{4}=3$rd value, Q1 = 17. Position of Q3 is $\frac{3n}{4}=9$th value, Q3 = 24. IQR=24 - 17 = 7.