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Data Representation and Interpretation

5.0 Data Handling and Probability · 5.1 Data Representation and Interpretation

Syllabus tag: Kenya CBC | Grade 8 Mathematics | Strand 5.0 Data Handling and Probability | Sub-Strand 5.1 Data Representation and Interpretation (10 lessons)

Lesson objectives

By the end of this sub-strand, you should be able to:

  • Draw and interpret bar graphs and line graphs of data
  • Recognise the mode from a set of discrete data
  • Calculate the mean of a set of discrete data
  • Determine the median of a set of discrete data

Data Representation and Interpretation

A list of numbers tells you little at a glance. A picture of the same numbers shows the pattern immediately.

a) Bar graphs

A bar graph compares separate categories. The height of each bar shows the count.

Goals scored in seven matches Goals scored in seven matches 0 1 2 3 0 1 2 3 matches goals

Bars for separate categories are usually drawn with gaps between them.

Label both axes and give the graph a title. An unlabelled graph cannot be read by anyone else.

Start the count axis at zero. Starting higher exaggerates the differences and misleads.

b) Line graphs

A line graph shows how something changes over time. Points are plotted and joined.

Temperature through the day Temperature through the day 0 2 4 6 8 10 12 0 5 10 15 20 25 30 hour °C

Use a line graph when the horizontal axis is continuous, such as time. Use a bar graph when the categories are separate.

Reading between the plotted points is reasonable for a line graph, because the quantity changed continuously in between.

c) Three kinds of average

An average is a single value that stands for a whole set.

Three kinds of average Three kinds of average the data = 4, 6, 7, 7, 9, 11, 12 seven values, in order mean = 56 / 7 add them, divide by how many mean = 8 the average value median = 7 the middle one when ordered mode = 7 the one that appears most

The mean is the total divided by how many values there are.

The median is the middle value once the data is put in order. With an even number of values, take the mean of the middle two.

The mode is the value that appears most often. A set can have more than one mode, or none at all.

d) Which average to use

The mean uses every value, but one extreme value drags it. One learner scoring 100 when everyone else scored around 30 pulls the mean up.

The median ignores extremes. It describes the typical value better when the data has one or two unusual entries.

The mode is the only average that works for things that are not numbers. Think of the most common shoe size, or a favourite colour.

e) Reading a graph

Check the title and both axis labels first.

Check the scale on each axis before reading any value.

Then ask what the shape tells you. Rising, falling, steady, or a peak somewhere.

f) Where this is used

A school plots exam performance across terms. A shopkeeper graphs daily sales to see the busiest day. A health worker tracks cases week by week.

Words to know

  • Mode -- the value that appears most often in a data set.
  • Mean -- the sum of all values in a data set divided by the number of values.
  • Median -- the middle value of a data set arranged in ascending order (or the mean of the two middle values, if the count is even).

:::checkpoint Check yourself

  1. When should you use a line graph rather than a bar graph?
  2. Find the mean of 5, 8, 8, 11.
  3. Find the median and mode of 3, 4, 6, 6, 9.
  4. Why can one very large value make the mean misleading? :::

Bridge to practice

Try the exercises below -- on interpreting graphs, and finding the mode, mean, and median of a data set.

Check yourselfPractise Data Representation and Interpretation — 10 questions →Next in MathematicsGeometrical Constructions →