The 35 learners in a Grade 7 class wrote an English test out of 60.

Table 1 summarizes the marks.

Use the data in table 1 to answer the following questions:

2.1. Is the data discrete or continuous? Substantiate your answer. (1)

2.2. Which graph(s) will best display this type of data? Substantiate your answer. (1)

2.3. Calculate the following:

2.3.1. the mean (correct to three decimal places) (2)

2.3.2. the median (2)

2.3.3. the mode (2)

2.4. Which is the better measure of the central tendency for this data - the mean or the median? Explain your answer. (1)

2.5. Calculate the following:

2.5.1. The variance (correct to three decimal places) (2)

2.5.2. The interquartile range (6)

2.6. Draw an ordered stem-and-leaf diagram to organize this data. (8)

2.7. Use class intervals 10 ? x ? 19, 20 ? x ? 29, 30 ? x ? 39, etc..., to construct a frequency table for the English test marks of the 35 learners.

A frequency table should have a tally column. (8)

2.8. Using the same frequency table drawn up in 2.7 and class boundaries of 10 ? x ? 19, 20 ? x ? 29, 30 ? x ?39, etc..., construct a histogram to represent the English test marks. (5)

2.9. From your histogram, determine the modal class of the English test marks. (1)

2.10. Is the data symmetrical, positively skewed, or negatively skewed? Explain your answer. (2)

2.11. Using the same frequency table as in 2.7 and class boundaries of 10 ? x ? 19, 20 ? x ? 29, 30 ? x ? 39, etc..., construct the following:

2.11.1. A cumulative frequency table (5)

2.11.2. A cumulative frequency polygon (5)

2.12. Use the cumulative frequency table and cumulative frequency polygon in 2.11 and answer the following questions:

2.12.1. What percentage of learners scored less than 49 marks in the test? (1)

2.12.2. What percentage of learners scored more than 59 marks in the test? (1)

2.13. Draw and label a box-and-whisker plot to illustrate the dispersion of the English test marks. (5)

Table 1: The marks of the English test 14 20 27 31 33 40 40 41 41 41 41 42 42 46 46 49 50 51 51 52 53 54 54 56 56 57 58 59 59 60 60 60 60 56 43