Grade 10 essential mathematics Statistics and Probability – Statistics I Notes

Specific learning outcomes

1. Identify and outline the sub-sub-strands:
   • Ungrouped data
   • Application of graphs of data
2. Draw a frequency distribution table for ungrouped data.
3. Determine mean, mode and median of ungrouped data.
4. Represent data using bar graphs, line graphs and pie charts.
5. Interpret data from bar graphs, line graphs and pie charts.
6. Appreciate importance of data organization and interpretation in making effective decisions.

What is statistics?

Statistics is the study of collecting, organising, summarising and interpreting data. In this subtopic we work with ungrouped data (lists of individual values) and learn how to present and read graphs so that we can make good decisions — for example at school, in a market or when planning community activities.

Ungrouped data and frequency distribution table

Ungrouped data is a simple list of individual measurements or observations (e.g., test scores of each student). A frequency distribution table shows each distinct value and how many times it occurs.

Example (Kenyan school): Test scores of 10 students

Raw data (out of 100): 68, 75, 82, 68, 90, 75, 82, 88, 74, 68

Step 1: List distinct values and count frequency.

Mean, Mode and Median (of ungrouped data)

Mean (average)

Mean = sum of all values ÷ number of values.

For the example: Sum = 68+75+82+68+90+75+82+88+74+68 = 770. Number of values = 10. Mean = 770 ÷ 10 = 77.0

Mode

Mode is the value that occurs most often. From the frequency table, 68 occurs 3 times (highest), so Mode = 68.

Median

Median is the middle value when data are ordered. For n = 10 (even), median = average of 5th and 6th ordered values.

Ordered data: 68, 68, 68, 74, 75, 75, 82, 82, 88, 90 5th = 75, 6th = 75 → Median = (75 + 75) ÷ 2 = 75

• Mean = 77.0
• Mode = 68
• Median = 75

Representing data: Bar graph, Line graph, Pie chart

Graphs help visualise patterns and compare categories quickly. Below are simple visuals drawn with SVG (works in most browsers).

Interpreting graphs and making decisions

After drawing graphs, ask:

• What is the most common value (mode)?
• Is the mean higher or lower than the median? (This can suggest skew.)
• What trends do line graphs show over time?
• What parts are largest or smallest in a pie chart?
• What action should be taken because of the data? (e.g., offer more revision classes for weak topics, buy more of a popular item in the school shop)

Example decision (school context): If a class shows low mean scores in Science and many students prefer Maths, the school may arrange more Science revision or resources to improve Science mean scores.

Suggested learning experiences (Kenyan context, age 15)

1. Class data collection:
   • Collect small ungrouped data sets from the class (e.g., number of siblings, exam scores, distance from home to school in km, favourite subject).
   • Construct frequency tables and compute mean, median and mode in pairs.
2. Graph drawing:
   • Create bar graphs and pie charts by hand or using a calculator/app; compare which graph type best shows the message.
3. Interpretation activity:
   • Provide printed graphs (bar, line, pie) showing e.g., corn harvest quantities in months or matatu passenger counts. Ask learners to write 3 conclusions and suggest one decision (e.g., buy more storage in high-harvest months).
4. Group project (community link):
   • Survey a local market for prices of a common commodity (e.g., a kg of maize) over a month. Present data as a line graph and explain trend to the class.
5. Reflection:
   • Discuss how organising data helped make clearer decisions — relate to Kenya examples (farm planning, school resource allocation).

Quick tips

• Always check that total frequency equals number of data points.
• For odd n, median is the middle value; for even n, median is average of two middle values.
• Use bar graphs for comparing categories, line graphs for trends over time, and pie charts for showing parts of a whole.
• Statistics supports decisions — organised data reduces guesswork.