Grade 12 MathLit - Data Handling: Statistics & Graphs Worksheet

Instructions: When describing a graph, always refer to specific values. For “compare” questions, mention both data sets. Refer to actual figures from the data in your answers.

Section A: Measures of Central Tendency (6 marks)

Monthly sales figures (in thousands of rands) for a small business over 10 months:

$42;\; 38;\; 55;\; 61;\; 38;\; 47;\; 52;\; 66;\; 38;\; 43$

1. Calculate the mean. (2)

2. Find the median. (2)

3. Identify the mode. (1)

4. Calculate the range. (1)

Section B: Histogram (6 marks)

A histogram shows the ages of 40 customers at a store:

1. Which age group has the highest frequency? (1)

2. What percentage of customers are aged 35 or older? (2)

3. Describe the shape of the distribution. (2)

4. In which age group does the median fall? (1)

Section C: Box-and-Whisker Plot (4 marks)

The five-number summary for a set of test marks is: Min = 32, Q1 = 48, Median = 61, Q3 = 74, Max = 95.

1. Draw a box-and-whisker plot for this data. (2)

2. Calculate the interquartile range (IQR). (1)

3. Are there any outliers if the fence is $Q1 - 1.5 \times IQR$ and $Q3 + 1.5 \times IQR$? Show your working. (1)

Section D: Describe & Compare (4 marks)

Class A: mean = 58%, median = 62%, range = 40%

Class B: mean = 58%, median = 51%, range = 18%

1. Both classes have the same mean. Which class had more consistent results? Give a reason. (2)

2. Class B has a median lower than its mean. What does this suggest about the distribution of marks? (2)

Total: 20 marks