Question

The table below shows the scores of a group of students on a 10-point quiz.Test ScoreFrequency3 54 15 16 27 28 49 310 1The mean score on this test is: _________________The median score on this test is: ____________________

Answer 1

Explanation

Part A

We can use the formula below to find the mean.

$\text{Mean}=\sum ^{}_{}(\frac{fx}{f})$

We will then have;

$\begin{gathered} \text{Mean = }\frac{5\times3+4\times1+5\times1+6\times2+7\times2+8\times4+9\times3+10\times1}{19}=\frac{15+4+5+12+14+32+27+10}{19} \\ =\frac{119}{19}=6.2632 \end{gathered}$

Mean = 6.2632

Part B

Since the data set is odd.

$\begin{gathered} \text{Median}=\frac{(n+1)}{2}^{th}\text{observation} \\ =\text{Value of }\frac{\text{(19+1)}}{2}^{th}\text{observation} \\ =\text{value of 10th observation} \end{gathered}$

Answer: From the column of cumulative frequency cf, the median is 7