Last reviewed: 11 November 2026
Updated November 2026. These Grade 8 data presentation notes show how to draw and interpret bar graphs and line graphs, and how to find the mode, mean and median of a set of discrete data. Discrete data are separate countable values, such as the number of books a learner read or the score on a ten-question quiz. A bar graph compares categories; a line graph shows how a value changes, often over time.
The examples are original practice for Kenyan junior school learners, not an official paper. They follow the Grade 8 Mathematics data handling sub-strand on data presentation and interpretation in the KICD Grade Eight curriculum designs. Grouped data, with class intervals and a modal class, is a Grade 9 topic covered in the Grade 9 grouped data notes. For Grade 8 topics overall, use the Grade 8 mathematics revision guide and the Grade 8 notes hub.
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Bar Graphs and Line Graphs
A bar graph uses bars of equal width, separated by gaps, whose heights match the frequencies. Choose a scale that fits the largest value and label both axes, including units. A line graph plots points and joins them in order, which is useful for a quantity that changes from one time or position to the next. OpenStax Introductory Statistics’ section on line graphs and bar graphs draws the same distinction.
Worked example: reading a bar graph
A class recorded favourite ball games: football 12 learners, netball 8, volleyball 5 and basketball 3.
- The scale on the frequency axis can go up in twos to at least 12.
- Football is the most popular game; basketball is the least popular.
- The total number of learners who answered is 12 + 8 + 5 + 3 = 28.
- Football and netball together account for 20 out of 28 learners.
Worked example: reading a line graph
A school weather club recorded midday temperature, in °C, from Monday to Friday: 22, 24, 21, 25, 23. Plot Monday to Friday on the horizontal axis and temperature on the vertical axis, then join the points. The graph rises from Monday to Tuesday, falls on Wednesday, peaks on Thursday at 25 °C, then drops slightly on Friday. The largest day-to-day change is the rise of 4 °C from Wednesday to Thursday.
Mode, Mean and Median of Discrete Data
For a list of separate values:
- The mode is the value that appears most often. A set can have more than one mode, or no mode if every value appears once.
- The mean is the total of the values divided by how many values there are.
- The median is the middle value after the data have been written in order. If there are two middle values, the median is their mean.
OpenStax Introductory Statistics’ section on measures of the centre defines mean and median in the same way.
Worked example: an odd number of scores
Seven quiz scores, already ordered, are 4, 7, 7, 9, 11, 12 and 14.
- Mode = 7, the only repeated score.
- Mean = (4 + 7 + 7 + 9 + 11 + 12 + 14) ÷ 7 = 64 ÷ 7 = 9 1/7.
- Median = the 4th value, 9.
Worked example: an even number of values
The number of books six learners read in a month is 3, 5, 8, 10, 12 and 15. There is no mode. The mean is 53 ÷ 6 = 8 5/6. The two middle values are 8 and 10, so the median is (8 + 10) ÷ 2 = 9.
Original Practice Questions With Worked Answers
- A bar graph shows mango 9, pineapple 6, orange 6 and banana 4 as favourite fruits. How many learners were asked, and which fruit shares the role of mode? 25 learners were asked. Mango is the clear favourite; pineapple and orange are tied on 6, but the mode of the fruit choices is mango because 9 is the highest frequency.
- Using the temperature list 22, 24, 21, 25, 23, what was the lowest midday temperature? 21 °C on Wednesday.
- Find the mode, mean and median of 2, 5, 5, 6, 7. Mode 5; mean 25 ÷ 5 = 5; median 5.
- Find the median of 11, 4, 9, 6. Ordered: 4, 6, 9, 11. Median = (6 + 9) ÷ 2 = 7.5.
- Why should the bars of a bar graph not touch? Gaps show that the categories are separate, not a continuous measurement along a scale.
- A learner finds the median of 4, 7, 7, 9, 11, 12, 14 by averaging 7 and 9. What went wrong? There are seven values, so there is a single middle value, 9. You only average two middle values when the count is even.
Cover the answers and try each question. Probability from chance experiments is the next data-handling topic, in the Grade 8 probability notes. For timed practice use the Grade 8 CBC Challenge. These notes are free; full revision access is available with the KSh 20 Day Pass or the KSh 500 Monthly Pass.
Frequently Asked Questions
What is the difference between a bar graph and a line graph?
A bar graph compares separate categories, such as favourite games. A line graph shows how a value changes in order, such as temperature from Monday to Friday.
How do you find the mean of discrete data?
Add every value and divide by how many values there are. The scores 4, 7, 7, 9, 11, 12 and 14 have mean 64 ÷ 7 = 9 1/7.
How do you find the median when there is an even number of values?
Write the values in order and average the two middle ones. For 3, 5, 8, 10, 12 and 15 the median is (8 + 10) ÷ 2 = 9.
What is the mode?
The mode is the value that appears most often. In 4, 7, 7, 9, 11, 12, 14 the mode is 7. If every value appears once, the set has no mode.