Question

fredrick hit 14, 18, 13, 12, 12, 16, 13, 12, 1, and 15 home runs in 10 seasons of play. which statements are correct? check all that apply. fredricks data set contains an outlier. the median value is 12 home runs. the mean value is about 12.6 home runs. the median describes fredricks data more accurately than the mean. the mean value stays the same when the outlier is not included in the data set.

Explanation:

Step1: Ordenar los datos

1, 12, 12, 12, 13, 13, 14, 15, 16, 18

Step2: Identificar el outlier

El valor 1 es un outlier ya que está muy alejado de los demás valores.

Step3: Calcular la mediana

Como hay 10 valores (un número par), la mediana es el promedio de los 5º y 6º valores ordenados. $\frac{13 + 13}{2}=13$.

Step4: Calcular la media

$\text{Media}=\frac{1+12 + 12+12+13+13+14+15+16+18}{10}=\frac{126}{10}=12.6$

Step5: Analizar la representatividad

Debido al outlier, la mediana es más representativa que la media, ya que la media se ve afectada por el valor extremo.

Step6: Analizar el cambio de la media sin el outlier

$\text{Media sin el outlier}=\frac{12 + 12+12+13+13+14+15+16+18}{9}=\frac{125}{9}\approx13.89$, la media cambia.

Answer:

• Fredrick's data set contains an outlier.
• The mean value is about 12.6 home runs.
• The median describes Fredrick's data more accurately than the mean.