Statistics Long Questions (Question 1)

Question 1:
The data below shows the age of 25 tourists who visited a tourist spot.
 2       25       8       15       19 17       4       28       10       16 16       18        19       7       28 14       22       20       6       26 24       16        8       11       30

(a) Copy and complete the table below based on the data above.
 Age (years) Frequency Midpoint 1 – 5 2 3 6 – 10
(b) Based on the completed table above,
(i) State the modal class.
(ii) Calculate the mean age of the tourists.
(c) For this part of the question, use graph paper.
By using a scale of 2cm to 5 years on the horizontal axis and 2cm to 1
tourist on the vertical axis, draw a histogram for the data.

Solution
:

(a)
 Age (years) Frequency Midpoint 1 – 5 2 3 6 – 10 5 8 11 – 15 3 13 16 – 20 8 18 21 – 25 3 23 25 – 30 4 28

Calculation of midpoint for (age 6 – 10) = $\frac{6+10}{2}=8$

(b)(i)
Modal class = age 16 – 20 (highest frequency)

(b)(ii)
$\begin{array}{l}\text{mean age =}\frac{3×2+8×5+13×3+18×8+23×3+28×4}{25}\\ \text{=}16.4\end{array}$ (c)