The monthly profit (in thousands of rands) made by a company in a year is given in the table below: 110 112 156 164 167 169 171 176 192 228 278 360 1.1 Calculate the: 1.1.1 Mean profit for the year 1.1.2 Median profit for the year 1.2 On the number line provided in the ANSWER BOOK, draw a box and whisker diagram to represent the data - NSC Mathematics - Question 1 - 2018 - Paper 2

To find the median, first, list the profits in ascending order:

110, 112, 156, 164, 167, 169, 171, 176, 192, 228, 278, 360.

Since there are 12 values (an even number), the median will be the average of the 6th and 7th values:

$\text{Median} = \frac{169 + 171}{2} = \frac{340}{2} = 170$

Thus, the median profit for the year is 170 thousand rands.

To draw a box and whisker diagram, first find the minimum (110), first quartile (Q1, 167), median (170), third quartile (Q3, 228), and maximum (360).

Next, plot these values on a number line and construct the box from Q1 to Q3, with a line at the median. Draw whiskers from the min to Q1 and from Q3 to the max.

The interquartile range (IQR) is calculated as follows:

$\text{IQR} = Q3 - Q1 = 228 - 167 = 61$

Therefore, the interquartile range of the data is 61 thousand rands.

The distribution appears to be positively skewed since the mean (179.17) is greater than the median (170). Additionally, there is a more significant spread on the higher end of the data (as observed with the max value of 360). This indicates that higher profits are influencing the distribution.

To find the standard deviation, first calculate the mean (179.17), then use the formula:

$\sigma = \sqrt{\frac{\sum (x_i - \mu)^2}{n}}$

Carry out this calculation with each of the data values to find:

$\sigma \approx 76.45$

One standard deviation below the mean is:

$179.17 - 76.45 \approx 102.72$

Review the profit data:

The profits less than 102.72 are none.

Thus, there are 0 months where the profit was less than one standard deviation below the mean.