SAT · Math · Problem-Solving and Data Analysis
Media, mediana, rango y cómo cambian cuando se añade o modifica un dato.
Datos 2, 4, 4, 5, 10: media = $25\div5=5$; mediana = 4.
Intenta responder antes de abrir la solución. Las preguntas están en el idioma del examen.
$$12,\ 5,\ 9,\ 15,\ 7,\ 20$$
What is the median of the data set shown?
Respuesta correcta: B. $10.5$
Order the values: $5, 7, 9, 12, 15, 20$. With six values, the median is the mean of the two middle values: $\frac{9+12}{2}=10.5$.
$9$ and $12$ are each only one of the two middle values. $12.5$ is the midpoint of the least and greatest values, $\frac{5+20}{2}$, not the median.
The mean of five numbers is 12. When a sixth number is added to the list, the mean of the six numbers is 13. What is the sixth number?
Respuesta numérica (escribes el número).
Respuesta: 18
The five numbers have a sum of $5\times12=60$. The six numbers have a sum of $6\times13=78$. The sixth number is $78-60=18$.
A data set consists of the five values $3$, $8$, $12$, $15$, and $x$. The mean of the data set is equal to its median. What is the sum of all possible values of $x$?
Respuesta numérica (escribes el número).
Respuesta: 33.5 · 67/2
The mean is $\frac{38+x}{5}$. The median depends on where $x$ falls.
If $x\le 8$, the median is $8$: $\frac{38+x}{5}=8$ gives $x=2$, which is $\le 8$, so it works.
If $8\le x\le 12$, the median is $x$: $\frac{38+x}{5}=x$ gives $x=9.5$, which is between $8$ and $12$, so it works.
If $x\ge 12$, the median is $12$: $\frac{38+x}{5}=12$ gives $x=22$, which is $\ge 12$, so it works.
The sum of all possible values is $2+9.5+22=33.5$.