(2.3) Data Handling and Algebra — Numeracy

These are the tools of logic, analysis, and prediction.

Whether calculating class terminal average, analysing a C.A. frequency curve, or structuring a logical problem via an equation, these two domains are non-negotiable for professional practice.

1. Types of Data

Qualitative data

Non-numerical attributes or labels (e.g., student gender, blood groups, favourite school subjects).

Quantitative data

Measurable values that can be counted or ordered.

• Discrete: Countable, isolated values (e.g., number of students in a class: 35, 36—never 35.5).
• Continuous: Measurable values along a continuous scale (e.g., student height: 1.65m, or weight: 54.3kg).

2. Construction and Interpretation of Charts

Bar charts

Used for discrete or qualitative data.

Columns are separated by gaps.

Pie charts

Circular representations of parts of a whole (100% or 360°)

Line graphs

Best used to track changes, trends and continuous data over time (e.g., school enrolment from 2020 to 2026).

3. Measures of Central Tendency

These metrics identify the single “centre” or representative value of a dataset.

Sample question: A group of five JSS3 students scored the following marks in a 10-point math quiz: 4, 7, 4, 9, 6. Calculate the Mean, Median, and Mode.

See workings:

Mean (average)

• Sum all values (Σx) and divide by the total count (n).

Median (middle)

• First, arrange the data in ascending or descending order: 4, 4, 6, 7, 9.

The middle position value is 6. (But If total number is even, find the mean of the two middle values).

Mode (most frequent)

• Identify the value that appears most often.
  • The number 4 occurs twice, while others occur once.

Mode = 4

4. Frequency Distributions

Histogram

Used for grouped, continuous data.

Unlike a bar chart, the bars touch each other, and the area of each bar is proportional to its frequency class interval.

Cumulative Frequency (Ogive)

A line graph that tracks running totals of frequencies. It is used to quickly locate the Median (50th percentile), Lower Quartile (Q1), and Upper Quartile (Q3).

5. Measures of Dispersion

These metrics analyse how scattered or packed the data points are around the mean.

Range

The simplest measure.

• Range = Maximum Value – Minimum Value.

Variance (σ²) and Standard Deviation (σ)

Standard deviation measures the average distance of each data point from the mean.

A low standard deviation means student scores are uniform; a high standard deviation means wide performance gaps in the classroom.

6. Simple Probability

Probability measures the likelihood of an event occurring, bounded strictly between 0 (impossible) and 1 (certainty).

Sample question: A box contains 8 blue pens, 5 red pens, and 7 black pens. If a teacher picks one pen at random, what is the probability that it is not a red pen?

See workings:

• Find the total number of possible outcomes (total pens)
  • Total: 8 + 5 + 7 = 20 pens
• Find the successful outcomes (pens that are not red = blue + black)
  • Not Red = 8 + 7 = 15 pens
• Apply the probability formula and simplify the fraction
  • P (Not Red) = 15/20 (i.e., 3/4 or 0.75 or 75%)

7. Identifying and Extending Patterns

Linear patterns (Arithmetic)

Change happens by adding or subtracting a constant difference (d).

• Example: 3, 7, 11, 15, …
  • (Adding 4 each time. Next term is 19).

Non-Linear patterns (Geometric)

Change happens by multiplying or dividing by a constant ratio (r), or by shifting through square numbers.

• Example: 2, 6, 18, 54, …
  • (Multiplying by 3 each time. Next term is 162).

8. Equations

Linear equation (1 variable)

Sample question: Solve for x in 3(x – 4) = 5x + 2

See workings:

• Expand the bracket using the distributive property
  • 3x – 12 = 5x + 2
• Collect like terms (move 3x to the right, and 2 to the left)
  • -12 – 2 = 5x – 3x
  • -14 = 2x
• Divide both sides by 2
  • x = -14/2 = -7

Simultaneous equations (2 variables)

Sample question: Find the values of x and y using the elimination method:

• 2x + y = 7
• 3x – y = 3

See workings:

• Because the coefficients of y are identical but opposite in sign (+y and -y), add equation (1) and equation (2) together to eliminate y:
  • (2x + 3x) + (y – y) = 7 + 3
  • 5x = 10
  • x = 2
• Substitute x = 2 back into equation (1) to solve for y:
  • 2(2) + y = 7
  • 4 + y = 7 → y = 7 – 4
  • y = 3

Answer: x = 2, y = 3

Quadratic equations (ax² + bx + c = 0)

Quadratic equations can be solved using factorization or the quadratic formula:

Sample question: Solve for x by factorization: x² – 5x + 6 = 0

See workings:

• Find two numbers that multiply to give +6 (the constant term) and add to give -5 (the middle coefficient).
  • Those numbers are -2 and -3 (since -2 × -3 = 6 and -2 + -3 = -5).
• Rewrite the equation in factored form:
  • (x – 2) (x – 3) = 0
• Set each factor to zero:
  • x – 2 = 0 → x = 2
  • x – 3 = 0 → x = 3

Answer: x = 2 or x = 3

Numeracy Application Strategy

If an exam question asks: “A student receives an assignment grade distribution showing that the median score is much higher than the mean score. What does this tell you about the class performance?”

Wrong: Most of the students failed the test.

Right: A few students scored exceptionally low marks, pulling the mean downward (negative skew), while more than half of the class performed quite well above that average.