12.2.1 Measures of Central Tendencies, PT3 Focus Practice

12.2.1 Measures of Central Tendencies, PT3 Focus Practice

Question 1:
Given that the mode of the set of data 7, 5, 3, 2, 3, y, 7, 6 and 5 is 7, find the mean.

Solution:
If the mode is 7, then y = 7
$\begin{array}{l}\therefore \text{Mean}=\frac{7+5+3+2+3+7+7+6+5}{9}\\ \text{}=\frac{45}{9}\\ \text{}=5\end{array}$

Question 2:
The mean of the set of numbers 7, 2, x, 4, 5, 3, y is 5. The value of x + y is

Solution:
$\begin{array}{l}\text{Mean =}\frac{\text{sum of all values of data}}{\text{total number of data}}\\ \\ \frac{7+2+x+4+5+3+y}{7}=5\\ \therefore x+y+21=7×5\\ \text{}x+y=35-21\\ \text{}x+y=14\end{array}$

Question 3:
Table below shows the number of story books read by a group of pupils in a week.

 Number of books 1 2 3 4 5 Number of pupils 3 0 1 5 6
The median of the data is

Solution:

 Number of books 1 2 3 4 5 Number of pupils 3 0 1 5 6 Position 1 – 3 3 4 5 – 9 10 – 15
Number of pupils = 3 + 0 + 1 + 5 + 6 = 15
Middle position situated at 8th.
From the table, the position 8 has a value of 4, therefore the median of the data is 4.