Calculate the mean, median, range, IQR, and mode for Thandiwe's and Anna's marks.

There are $n=10$ marks.

• Mean: Sum of marks divided by the number of marks. $$\text{Mean} = \frac{3+5+10+10+11+12+14+16+19+20}{10} = \frac{120}{10} = 12$$
• Median: The middle value of the sorted data. Since there are 10 marks (an even number), the median is the average of the 5th and 6th values. $$\text{Median} = \frac{11+12}{2} = \frac{23}{2} = 11.5$$
• Range: The difference between the highest and lowest marks. $$\text{Range} = 20 - 3 = 17$$
• Mode: The mark that appears most frequently. $$\text{Mode} = 10$$
• Interquartile Range (IQR): The difference between the upper quartile (Q3) and the lower quartile (Q1). Q1 is the median of the lower half of the data ($3, 5, 10, 10, 11$), so $Q1 = 10$. Q3 is the median of the upper half of the data ($12, 14, 16, 19, 20$), so $Q3 = 16$. $$\text{IQR} = Q3 - Q1 = 16 - 10 = 6$$ Thandiwe's results: Mean = $\boxed{12}$, Median = $\boxed{11.5}$, Range = $\boxed{17}$, Mode = $\boxed{10}$, IQR = $\boxed{6}$.

There are $n=10$ marks.

• Mean: Sum of marks divided by the number of marks. $$\text{Mean} = \frac{11+11+11+12+12+12+12+13+13+13}{10} = \frac{120}{10} = 12$$
• Median: The middle value of the sorted data. Since there are 10 marks, the median is the average of the 5th and 6th values. $$\text{Median} = \frac{12+12}{2} = \frac{24}{2} = 12$$
• Range: The difference between the highest and lowest marks. $$\text{Range} = 13 - 11 = 2$$
• Mode: The mark that appears most frequently. $$\text{Mode} = 12$$
• Interquartile Range (IQR): The difference between the upper quartile (Q3) and the lower quartile (Q1). Q1 is the median of the lower half of the data ($11, 11, 11, 12, 12$), so $Q1 = 11$. Q3 is the median of the upper half of the data ($12, 12, 13, 13, 13$), so $Q3 = 13$. $$\text{IQR} = Q3 - Q1 = 13 - 11 = 2$$ Anna's results: Mean = $\boxed{12}$, Median = $\boxed{12}$, Range = $\boxed{2}$, Mode = $\boxed{12}$, IQR = $\boxed{2}$.