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 values $4$, $7$, $7$, $9$, $12$, $15$, and $x$, where $x>15$. The mean of the data set is $2$ greater than the median. What is the value of $x$?
Respuesta numérica (escribes el número).
Respuesta: 23
Because $x>15$, the values in order are $4, 7, 7, 9, 12, 15, x$, and the median (the 4th of $7$ values) is $9$. The mean is therefore $9+2=11$, so the sum of the $7$ values is $7\times 11=77$. The other six values add up to $54$, so $x=77-54=23$.