Question

5. Respond to the following questions about statistics.(a) Find the mean, median, and mode of the following dataset:{10,20, 42, 22, 56, 42, 3, 89, 42, 70,20}

Answer 1

Given:

A data set: {10,20, 42, 22, 56, 42, 3, 89, 42, 70,20}.

TO find:

The mean, median and mode.

Solution:

The mean of a data set is given by:

$Mean=\frac{\text{ sum of all observations}}{\text{ number of observations}}$

So, the mean for the given data set is:

$\begin{gathered} Mean=\frac{10+20+42+22+56+42+3+89+42+70+20}{11} \\ =\frac{416}{11} \\ =37.82 \end{gathered}$

To find the median, first change them into ascending order as

3, 10, 20, 20, 22, 42, 42, 42, 56, 70, 89.

Now, the number of observations is odd. So, the median of the data set is:

$\begin{gathered} Median=\frac{n+1}{2}th\text{ term} \\ =\frac{11+1}{2}th\text{ term} \\ =6th\text{ term} \\ =42 \end{gathered}$

Now, the element whose frequency is maximum is the mode of the given data set. Here, the frequency of 42 is maximum. So, the mode is 42.

Thus, the mean is 37.82, the median is 42 and the mode is 42.