The figures in the table below are the ages, to the nearest year, of a random sample of 30 people negotiating a mortgage in a bank. Use the data below to answer the questions that follow.

Key: $11 \ | \ 0 = 110 \text{ cm}$

1.2 Determine the:

1.2.1 Median

The median is the average of the $9^{th}$ and $10^{th}$ values.

1.2.2 Mode

The values 129 and 162 each appear twice, which is more than any other value.

1.2.3 Lower quartile and the upper quartile

This is the median of the lower half of the data.
The lower half consists of the first 9 values: $110, 125, 128, 129, 129, 130, 131, 133, 139$.
$Q_1$ is the $\left(\frac{9+1}{2}\right)^{th} = 5^{th}$ value of this lower half.

This is the median of the upper half of the data.
The upper half consists of the last 9 values: $142, 143, 147, 151, 152, 153, 162, 162, 165$.
$Q_3$ is the $\left(\frac{9+1}{2}\right)^{th} = 5^{th}$ value of this upper half.

1.2.4 Mean

Question 2

The given data for ages are:
$29, 26, 31, 42, 38, 45, 35, 37, 38, 38, 36, 39, 49, 40, 32, 32, 34, 27, 56, 29, 33, 31, 33, 52, 44, 32, 30, 38, 42, 33$.
There are $N=30$ data points.

2.1 Complete the frequency table.

• For $25 \le x < 33$: $29, 26, 31, 32, 32, 27, 29, 31, 32, 30$ (10 values)
• For $33 \le x < 41$: $38, 35, 37, 38, 38, 36, 39, 40, 34, 33, 33, 38, 33$ (13 values)
• For $41 \le x < 49$: $42, 45, 44, 42$ (4 values)
• For $49 \le x < 57$: $49, 56, 52$ (3 values)

2.2 Use the information from the frequency table to draw a histogram.

2.3 Draw a frequency polygon on the grid provided in the SPECIAL ANSWER SHEET.

These parts require a special answer sheet with a grid, which is not provided here. Therefore, these cannot be completed in this format.