the fuel economies in miles per gallon (mpg) for nine vehicles are listed below. 16, 18, 20, 24, 24, 24, 24…

the fuel economies in miles per gallon (mpg) for nine vehicles are listed below. 16, 18, 20, 24, 24, 24, 24, 31, 32. if one more vehicle is added to the list with a rate of 40 mpg, how will this affect the mean and median? the mean and median will both increase. the mean will increase and the median will decrease. the mean will increase and the median will not change. the mean will decrease and the median will not change.

the fuel economies in miles per gallon (mpg) for nine vehicles are listed below. 16, 18, 20, 24, 24, 24, 24, 31, 32. if one more vehicle is added to the list with a rate of 40 mpg, how will this affect the mean and median? the mean and median will both increase. the mean will increase and the median will decrease. the mean will increase and the median will not change. the mean will decrease and the median will not change.

Answer

Explanation:

Step1: Calcular la media original

La media de un conjunto de datos $x_1,x_2,\cdots,x_n$ se calcula como $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$. Aquí $n = 9$, y $\sum_{i=1}^{9}x_i=16 + 18+20 + 24+24+24+24+31+32=213$. Entonces la media original $\bar{x}_1=\frac{213}{9}\approx23.67$.

Step2: Calcular la mediana original

Los datos ya están ordenados. Para $n = 9$ (un número impar), la mediana es el valor del $\left(\frac{n + 1}{2}\right)$ - ésimo término. $\frac{9+1}{2}=5$, así que la mediana original $M_1 = 24$.

Step3: Calcular la media con el nuevo dato

Ahora $n=10$, y $\sum_{i = 1}^{10}x_i=213 + 40=253$. La nueva media $\bar{x}_2=\frac{253}{10}=25.3$.

Step4: Calcular la mediana con el nuevo dato

Con $n = 10$ (un número par), la mediana es el promedio de los $\frac{n}{2}$ - ésimo y $\left(\frac{n}{2}+1\right)$ - ésimos términos. Los datos ordenados son $16,18,20,24,24,24,24,31,32,40$. $\frac{n}{2}=5$ y $\frac{n}{2}+1 = 6$, entonces $M_2=\frac{24 + 24}{2}=24$.

Answer:

The mean will increase and the median will not change.