DATA HANDLING AND PROBABILITY Notes, Quizzes & Revision
๐ Revision Notes โข ๐ Quizzes โข ๐ Past Papers available in app
SUBTOPIC: DATA HANDLING AND PROBABILITY
Subject: subject_replace | Topic: topic_name_replace | For learners aged age_replace (Kenyan context)
Learning objectives
- Collect and record data using simple tools (tally, tables).
- Organise data into frequency tables, pictographs and bar charts.
- Find mean, median, mode and range of small data sets.
- Understand basic probability: sample space, event and simple probabilities.
- Relate probability to everyday Kenyan situations (school, weather, market).
Key terms
Tally: Marks used to count items (||||).
Frequency: How often a value occurs.
Pictograph: Picture symbols used to show data (1 symbol = fixed number of items).
Bar chart: Bars that show frequency of each category.
Mean (average): Sum of values รท number of values.
Median: Middle value when data are ordered.
Mode: Most frequent value(s).
Range: Difference between highest and lowest values.
Sample space (S): All possible outcomes.
Probability P(E): Number of favourable outcomes รท total outcomes.
Frequency: How often a value occurs.
Pictograph: Picture symbols used to show data (1 symbol = fixed number of items).
Bar chart: Bars that show frequency of each category.
Mean (average): Sum of values รท number of values.
Median: Middle value when data are ordered.
Mode: Most frequent value(s).
Range: Difference between highest and lowest values.
Sample space (S): All possible outcomes.
Probability P(E): Number of favourable outcomes รท total outcomes.
1. Collecting and recording data
- Use simple surveys in class or at home. Example: Ask 20 classmates their favourite fruit from {Mango, Banana, Orange, Pineapple}.
- Record answers immediately using tally marks in a table.
- Record answers immediately using tally marks in a table.
Example: Favourite fruit (20 learners)
| Fruit | Tally | Frequency |
|---|---|---|
| Mango | |||| || | 7 |
| Banana | |||| | | 6 |
| Orange | || | 2 |
| Pineapple | |||| | 5 |
| Total | 20 |
2. Showing data visually
- Pictograph: choose one picture to represent a fixed number, e.g., ๐ = 2 learners.
Pictograph (1 picture = 2 learners)
Mango: ๐๐๐ + (one half) โ represent 7 by 3 full pictures and 1 half (3.5 ร 2 = 7)
Banana: ๐๐๐ โ 6
Orange: ๐ โ 2
Pineapple: ๐๐๐ (but if 1 picture = 2 learners, 5 learners = 2 full + half) โ ๐๐ยฝ
(You may draw half symbols when counts are odd.)
Banana: ๐๐๐ โ 6
Orange: ๐ โ 2
Pineapple: ๐๐๐ (but if 1 picture = 2 learners, 5 learners = 2 full + half) โ ๐๐ยฝ
Bar chart (frequency)
Mango
7
7
Banana
6
6
Orange
2
2
Pineapple
5
5
(Heights are proportional to frequency)
3. Mean, Median, Mode and Range
Example: Marks of 7 pupils in a quiz: 6, 8, 9, 7, 10, 8, 6 (Kenyan primary example).
- Mode โ the most common value. Here: 6 and 8 both appear twice โ modes = 6 and 8.
- Median โ middle value when data are ordered. Order: 6,6,7,8,8,9,10 โ middle is 8 โ median = 8.
- Mean โ add all marks then divide by number of pupils:
Sum = 6+8+9+7+10+8+6 = 54. Mean = 54 รท 7 โ 7.7
- Range โ highest โ lowest = 10 โ 6 = 4.
4. Basic Probability
- Probability measures how likely an event is. Always between 0 (impossible) and 1 (certain).
- Formula for a simple situation: P(Event) = Number of favourable outcomes รท Total number of possible outcomes.
- Formula for a simple situation: P(Event) = Number of favourable outcomes รท Total number of possible outcomes.
Examples:
- Flip a fair coin: S = {Heads, Tails}. P(Heads) = 1/2 = 0.5.
- Roll a fair six-sided die: S = {1,2,3,4,5,6}. P(roll a 4) = 1/6.
- Pick one pupil at random from a class of 30 where 12 play football. P(pupil plays football) = 12/30 = 2/5 = 0.4.
Link to data handling (relative frequency)
- If you observe that it rained on 9 out of 30 days in a month at school, the experimental probability of rain that month is 9/30 = 0.3. Over many months, relative frequency approaches true probability.
Practice questions (with quick answers)
- From the earlier fruit data (Mango 7, Banana 6, Orange 2, Pineapple 5), what is the probability that a randomly chosen learner prefers Banana?
Answer: 6/20 = 3/10 = 0.3
- Find the mean of marks: 4, 6, 6, 7, 9.
Answer: Sum = 32, mean = 32/5 = 6.4
- A spinner has equal sections coloured red, blue, green. What is the probability it lands on green?
Answer: 1/3
- Order these values and find the median: 12, 7, 9, 10, 8.
Answer: Ordered: 7,8,9,10,12 โ median = 9
Tips & Kenyan context
- Use local examples (school crops, market prices, rainfall days, sports teams) to collect data.
- When drawing pictographs for community data, make one picture represent a convenient number (2, 5 or 10) so symbols stay neat.
- Teach probability with classroom games: coin tosses, dice games, or drawing sweets from a bag.
- Encourage learners to check whether experimental probability (from surveys) matches theoretical probability for simple experiments.
Quick summary
Data handling helps collect, organise and display information. Probability tells us how likely events are. Together they help learners make sense of everyday situations โ from weather patterns in a Kenyan county to choices made in a school canteen.
Notes prepared for: subject_replace โ Topic: topic_name_replace โ Subtopic: DATA HANDLING AND PROBABILITY (Kenyan examples; for learners aged age_replace).