Data Presentation and Interpretation

Everyone, let's dive into frequency tables – a simple way to organize raw data before we start graphing. First, a frequency tells us how many observations fall into each class interval. Think of it like counting how many farms produce a certain range of milk each week. We create a frequency table by: (1) deciding the class intervals, (2) counting the observations in each interval, (3) writing those counts as frequencies, and (4) adding totals and cumulative frequencies. Here's our example table showing weekly milk production for three farms in Nakuru. Notice the 'Frequency' column and the 'Cumulative Frequency' at the right – the totals help us see overall trends. When you look at the cumulative column, you can quickly answer questions like 'How many farms produced less than 20 litres?' – just read the cumulative value for the interval just below 20.

Class, let's dive into bar graphs. We'll see how to turn a simple frequency table into a clear visual picture. First, we take the frequency table—like a list of how many students chose each sport—and represent each category with a vertical bar. Remember, for categorical data we use vertical bars. This helps us compare the categories side by side. Here is our bar graph showing the number of students who prefer each sport in a Kenyan secondary school. Notice the height of each bar corresponds to the count of students. The vertical axis is labeled 'Number of Students'—that tells us the scale we read from. The horizontal axis lists the sports categories—those are our labels. The title, 'Students' Favourite Sport (N=120)', reminds us this graph summarises data from 120 pupils. To answer questions, compare the heights: which sport is most popular? Which is least? Just look at the tallest and shortest bars.

Class, let's dive into line graphs – the tool we use whenever we want to see how something changes over time. Remember, we use a line graph for continuous data, like temperature throughout a day or rainfall over the months. Connecting the points lets us see the overall trend. Here's our example: monthly rainfall in Kitale for a year. Notice how the line rises in April and May, then drops sharply in August – that tells us the wet and dry periods. If you look at the grid, you can read the exact rainfall value for any month. For example, in November the line meets the grid at about 85 mm. To recap: line graphs show continuous data, we connect points to see direction and slope, and we can pull precise numbers from the grid. Any questions before we move on?

Let's explore pie charts – a simple way to show how parts make up a whole. First, we turn raw frequencies into percentages, then multiply each percentage by 3.6 to get the angle in degrees. In formula terms, Angle = Percent × 3.6. For example, a 25% share becomes 25 × 3.6 = 90°. Here's a pie chart of market share for three fruit vendors in Mombasa. Notice how each slice's size matches its percentage. Make sure each slice is clearly labelled with its percentage – that way anyone can read the chart at a glance. Can anyone tell me which vendor has the largest portion and which has the smallest? Take a moment to look and think.

Let's talk about histograms, the tool we use to display the distribution of continuous data. First, notice the difference between a bar graph and a histogram: the bars in a histogram touch each other because the data are grouped into adjacent class intervals. Here is a column chart that shows the histogram of Form 2 mathematics test scores. Each bar represents a class interval of scores. Choosing an appropriate class width is important – too wide and you lose detail, too narrow and the chart becomes noisy. In this example we used a width of 5 marks. Looking at the shape, we can see the distribution is slightly right‑skewed, meaning most students scored around the lower to middle range, with a few higher scores pulling the tail to the right. To recap, a histogram groups continuous data into touching bars, the class width determines the granularity, and the overall shape tells us about skewness and modality.

Everyone, let's dive into measures of central tendency and range. These tools help us summarise data, like the amount of milk a farmer produces each week. First, the mean is simply the total sum divided by the number of observations. Think of it as the average daily milk yield if you spread the total across all days. Next, the mode is the value that appears most often—the most common milk yield you might see week after week. The median is the middle value when you line up all the observations from smallest to largest. It tells us the central point that splits the data in half. Finally, the range is the difference between the maximum and minimum values. It shows us how spread out the milk production can be. Let's work through a real example using weekly milk production data. We'll calculate the mean, mode, median, and range together, step by step.