DATA HANDLING AND PROBABILITY Notes, Quizzes & Revision

1. What this subtopic covers

Data handling — how we collect, organise, display and summarise information (for example: number of passengers in a matatu, rainfall amounts in a month, scores in a test). Probability — how likely events are to happen (for example: the chance of picking a red fruit from a basket, or getting a 6 when throwing a die).

2. Key vocabulary

• Tally and frequency
• Table, pictograph, bar chart, pie chart, line graph
• Mean (average), median, mode, range
• Experiment, outcome, sample space, event
• Probability: P(event) = favourable outcomes / total outcomes
• Complement (not event), equally likely, relative frequency

3. Collecting and organising data

Use tally marks when you count items on the spot. Convert tallies to a frequency table.

Fruit     Tally    Frequency
Mango     ||||     4
Banana    ||||| || 7
Apple     ||||     4
Pear      ||       2
      

4. Graphical displays

Choose a display that matches your data:

• Pictograph — good for small whole-number counts (use a simple picture symbol).
• Bar chart — compare groups (like number of students in houses or passengers per matatu).
• Pie chart — show parts of a whole (percentages or fractions).
• Line graph — show change over time (monthly rainfall, daily temperatures).

5. Measures of centre and spread

Use these to summarise data:

• Mode — value that appears most often (e.g., most common shoe size).
• Median — middle number when data are ordered. If even count, median is average of two middle values.
• Mean (average) — total of values ÷ number of values. Use when values are roughly similar in size.
• Range — largest value minus smallest value (shows spread).

6. Probability — the basics

Probability tells how likely an event is. Write P(event). For equally likely outcomes:

P(event) = number of favourable outcomes / total number of outcomes

• Probability values are between 0 (impossible) and 1 (certain). You can also write them as fractions, decimals or percentages.
• Complement rule: P(not A) = 1 − P(A).
• Relative frequency: if you repeat an experiment many times, probability ≈ (times event occurred) / (total trials).

7. Simple examples (Kenyan context)

1. Coin toss: P(heads) = 1/2.
2. One die: P(6) = 1/6. P(odd number) = 3/6 = 1/2.
3. Basket with 3 mangoes, 2 oranges, 5 bananas: total 10 fruits. P(orange) = 2/10 = 1/5.
4. Pick a pupil at random from a class of 40 where 10 are in the football team: P(football) = 10/40 = 1/4.

8. Combined events (short note)

For independent events A and B (outcome of A does not change B): P(A and B) = P(A) × P(B). For example, tossing two coins: P(both heads) = 1/2 × 1/2 = 1/4.

9. Problem-solving tips

• Read the question carefully. Decide what is being asked (probability? average? display?).
• Write tallies when collecting data to avoid mistakes.
• Order numbers before finding median. Check units (e.g., cm, mm, passengers).
• For probability, list the sample space first if unsure.
• Always simplify fractions and, if useful, convert to percentage.

10. Practice questions (try these)

1. In a Nairobi market, a vendor records 8 mangoes, 6 bananas, 6 oranges. Make a frequency table and find the mode.
2. A die is thrown once. What is the probability of getting an even number? Give answer as fraction and percentage.
3. Class scores: 56, 48, 72, 64, 56 — find mean, median, mode and range.
4. A bag has 4 red, 3 blue and 3 green beads. One bead is picked at random. Find P(not red).
5. Two coins are tossed. List the sample space and find the probability of getting exactly one head.