LINEAR EQUATIONS

Activity 3: Analysis

Observe the following table:

Sr. No.	No. of Seeds (n)	Distance (L)	Average (x̅ - x bar)
1	5	1.1 cm (11 mm)	2.2 mm
2	10	2.1 cm (21 mm)	2.1 mm
3	15	3.2 cm (32 mm)	2.13̅ mm
4	20	4.2 cm (42 mm)	2.1 mm
5	25	5.2 cm (52 mm)	2.0 mm
6	30	6.4 cm (64 mm)	2.1 mm

You might have made a similar table. In the table above, we have added a fourth column for mentioning the 'average diameter' of the seeds. We will now see how the average is calculated.

For 5 seeds, the total length is 11 mm. Hence, the average length of each seed will be 11 mm ÷ 5 = 2.2 mm. Similarly, the average values for other entries in the table are calculated and mentioned in the last column. You can also use spreadsheets for maintaining the tables and calculating the average values.

Analysis with the help of graphs:

In the next step, we will use graphs to plot the data in the tables. Graphs provide a useful way to analyse our data and find the average diameter.

First, we will see how to use GeoGebra to plot graphs from the data we have:

Step 1: Open the GeoGebra application.

Step 2: For the first entry, the length of 5 seeds is 11 mm. Hence, we will plot point (5,11) on the graph using the Input tool. (See the video (GIF) below to know how to plot points in GeoGebra).

Step 3: Plot the points for the other values in the table.

After entering all the table data, we will get a graph like this:

Replay Animation

Step 4: After all the points are plotted, we will use the line tool to draw a line through all the points. This line should be such that, as much as possible, it should pass through all the points.

Replay Animation

In this way, we got a table and a graph using the example of mustard seeds. Now, try drawing graphs for the other tables made by you on the same graph.

Here is an example of how we plotted graphs for both seeds (mustard and jowar):

Discuss these questions on the graph with your buddies and write them in the space provided:

Q1. Does the combined length increase or decrease when the number of seeds increases?

Q2. Can we say that the numbers of seeds and their length are directly proportional?

Q3. Can you think of any situation in which when one quantity increases, another related quantity decreases?

Q4. Is it possible to find the length of a given number of seeds, say 100, from the graph?

[Hint: look for the Y coordinate from the graph]. You can also find this length by using an equation. In your answer, please mention how you found out this length: using the graph or by using the equation.

Export the graphs that you have drawn to an image and upload them in the gallery:

In the next activity, we will learn how to make equations for our data.