Question

elena mailed 6 packages, with the following shipping charges. $6.15, $4.78, $5.61, $4.41, $4.21, $6.54. if she mails a 7th package for $5.61, how will that affect the median shipping charge? choose 1 answer: a the median will remain the same. b the median will increase by $0.05. c the median will increase by $0.41. d the median will increase by $0.60.

Explanation:

Step1: Arrange initial 6 - value data in ascending order

$4.21,4.41,4.78,5.61,6.15,6.54$
Since $n = 6$ (even), median formula is $\text{Median}=\frac{x_{\frac{n}{2}}+x_{\frac{n}{2}+1}}{2}$. Here, $\frac{n}{2}=3$ and $\frac{n}{2}+1 = 4$. So, $\text{Median}=\frac{4.78 + 5.61}{2}=\frac{10.39}{2}=5.195$.

Step2: Add 7th value and arrange new data in ascending order

$4.21,4.41,4.78,5.61,5.61,6.15,6.54$
Since $n = 7$ (odd), median formula is $\text{Median}=x_{\frac{n + 1}{2}}$. Here, $\frac{n+1}{2}=\frac{7 + 1}{2}=4$. So, $\text{Median}=5.61$.

Step3: Calculate the change in median

Change in median $=5.61-5.195 = 0.41$

Answer:

C. The median will increase by $0.41$.