Revision (Grade 11 NSC Matric Mathematics): Revision Notes

Worked Example: Computing measures of central tendency

Question: Compute the mean and median of the following dataset: 72,5 ; 92,6 ; 15,6 ; 53,0 ; 86,4 ; 89,9 ; 90,9 ; 21,7 ; 46,0 ; 4,1 ; 51,7 ; 2,2

Solution:

Step 1: Calculate the mean

First, add all values together and divide by the number of values (12):

• $\bar{x} = \frac{626,6}{12} ≈ 52,22$

Step 2: Calculate the median

First, sort the data in ascending order:

• 2,2 ; 4,1 ; 15,6 ; 21,7 ; 46,0 ; 51,7 ; 53,0 ; 72,5 ; 86,4 ; 89,9 ; 90,9 ; 92,6

Since there are 12 values (even number), the median lies between the 6th and 7th values.

The middle values are 51,7 and 53,0.

Therefore: Median = $\frac{51,7 + 53,0}{2} = 52,35$

Worked Example: Range and inter-quartile range

Question: Determine the range and inter-quartile range of the following dataset: 14 ; 17 ; 45 ; 20 ; 19 ; 36 ; 7 ; 30 ; 8

Solution:

Step 1: Sort the data

Ordered dataset: 7 ; 8 ; 14 ; 17 ; 19 ; 20 ; 30 ; 36 ; 45

Step 2: Find range

• Minimum value = 7
• Maximum value = 45
• Range = 45 - 7 = 38

Step 3: Find quartiles and IQR

From the quartile positions:

• Q₁ = 14 (first quartile)
• Q₂ = 19 (median)
• Q₃ = 30 (third quartile)

Inter-quartile range = Q₃ - Q₁ = 30 - 14 = 16

Worked Example: Five number summary

Question: Draw a box and whisker diagram for the following dataset: 1,25 ; 1,5 ; 2,5 ; 2,5 ; 3,1 ; 3,2 ; 4,1 ; 4,25 ; 4,75 ; 4,8 ; 4,95 ; 5,1

Solution:

Step 1: Identify minimum and maximum

• Minimum = 1,25
• Maximum = 5,1

Step 2: Calculate quartiles With 12 values in the dataset:

Using the quartile positions:

• Q₁ = $\frac{2,5 + 2,5}{2} = 2,5$
• Median = $\frac{3,2 + 4,1}{2} = 3,65$
• Q₃ = $\frac{4,75 + 4,8}{2} = 4,775$

Step 3: Five number summary

(1,25 ; 2,5 ; 3,65 ; 4,775 ; 5,1)

Step 4: Draw the box plot

The box plot shows the five number summary visually, with the box representing the middle 50% of the data and whiskers extending to the extremes.