Question

Jack's scores in $5$ quizzes are given as $57,63,55,61$, and $62$. If he scored $39$ in his sixth quiz, what will be the effect of his last score?

• A. The mean will increase due to the addition of low score.
• B. The median will decrease due to the addition of low score.
• C. The median will increase due to the addition of low score.
• D. The mean will decrease due to the addition of low score.

Answer 1

Answer: (B), (D)

The mean will decrease due to the addition of low score.

The data of Jack's score in first $5$ quizzes can represented as:


The mean of this data is calculated as,

$\begin{array}{cc}\text{Mean}& =\frac{\text{Sum of all data points}}{\text{Number of all data points}}\\ & =\frac{57+63+55+61+62}{5}\\ & =\frac{298}{5}\\ & =59.6\end{array}$

To find the median of this data, arrange the data in ascending order and observe the middle term.


Thus, the medain of this data is $61$.

Now in the presence of Jack's score in last quiz, i.e., $39$, the data will be given as:


Thus, the mean of this data is,

$\begin{array}{cc}\text{Mean}& =\frac{57+63+55+61+62+39}{6}\\ & =\frac{337}{6}\\ & =56.16\end{array}$

The median for even number of terms is obtained by arranging the given data in ascending order and finding the average of middle two terms. Thus, the median of this data is calculated as,


$\begin{array}{cc}\text{Median}& =\frac{57+61}{2}\\ & =\frac{118}{2}\\ & =59\end{array}$

The mean without lowest score is $59.6$ and with lowest score is $56.16$. While the median without lowest score is $61$ and with lowest score is $59$.

Hence, both mean and median decrease with the addition of low score.