Question

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

Explanation:

Step1: Ordenar los datos

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

Step2: Encontrar Q1 y Q3 para los 11 datos

Con 11 datos, el índice de Q1 es $\frac{11 + 1}{4}=3$, así que Q1 = 17. El índice de Q3 es $\frac{3(11 + 1)}{4}=9$, así que Q3 = 24. El rango intercuartil (IQR) original es 24 - 17=7.

Step3: Probar cada opción

Si agregamos 13: Los datos ordenados son 13, 13, 15, 17, 18, 20, 20, 21, 22, 24, 25, 27. Q1 = 15, Q3 = 22, IQR = 22 - 15 = 7.
Si agregamos 15: Los datos ordenados son 13, 15, 15, 17, 18, 20, 20, 21, 22, 24, 25, 27. Q1 = 15, Q3 = 22, IQR = 22 - 15 = 7 - 1=6.
Si agregamos 23: Los datos ordenados son 13, 15, 17, 18, 20, 20, 21, 22, 23, 24, 25, 27. Q1 = 17, Q3 = 23, IQR = 23 - 17 = 6. Pero al probar 15 se alcanza el IQR deseado primero.
Si agregamos 25: Los datos ordenados son 13, 15, 17, 18, 20, 20, 21, 22, 24, 25, 25, 27. Q1 = 17, Q3 = 24, IQR = 24 - 17 = 7.

Answer:

15