## Graphs – Line Graphs

 Image Credit: Pixabay.com

Graphs are visual representations of data collected. The purpose of a graph is to show numerical facts in visual form so that they can be understood quickly, easily and clearly. Graphical presentation of data is easier to understand particularly when there is a trend or comparison to be shown.

## Discrete and Continuous Data

Discrete data is a count that can’t be made more precise. Typically it involves integers. For instance, the number of children (or adults, or pets) in our family is discrete data, because we are counting whole, indivisible entities: we can’t have 2.5 kids, or 1.3 pets.

Continuous data, on the other hand, could be divided and reduced to finer and finer levels. For example, we can measure the height of the kids at progressively more precise scales—meters, centimeters, millimeters, and beyond — so height is continuous data.

Some data are continuous but measured in a discrete way e.g. our age.

Discrete data is countable & take only integer values while continuous data is measurable & can take any value (within a range).

# Graphs

We have discussed following types of graphs under GRAPHICAL REPRESENTATION OF DATA:

(i) Pictograph – It represents data through pictures or symbols of objects.

(ii) Bar Graphs/ Double Bar Graphs – A bar graph is used to show comparison among categories. It may consist of two or more parallel vertical (or horizontal) bars (rectangles).

(iii) Pie Graphs or Circle Graphs – A pie-graph is used to compare parts of a whole.

(iv) Histogram – A Histogram is a bar graph that shows data in intervals. It has adjacent bars over

the intervals. There are no gaps between bars, because there are no gaps between the intervals.

To know more about these👆 Graphs👈TAP

Bar graphs & Pie graphs display Discrete data whereas Histograms display Continuous data.

# Line Graph

A line graph displays continuous data as a series of data points (individual measurements) connected by straight line segments. It is often used to visualize a trend in data over periods of time.

### ⦿ Temperature – Time graph

A person fell sick, her doctor maintained a record of her body temperature, taken every four hours. The records put in tabular form and its pictorial representation (graph) are shown in figure given below-

 Line Graph

↪ The horizontal line is called the x-axis and the vertical line is called the y-axis.

↪ Using suitable scales, time & temperature are plotted on x-axis & y-axis respectively.

↪ Dots on the intersection of corresponding data of time & temperature called data points are placed. The points are then connected by line segments. The result is the line graph.

↪Interpretation/Analysis of graph –

By analyzing the graph above, we can interpret many useful information like –

* The temperature increases between 6 am to 10 am and then decreases between 10 am to 2 pm and further decreases between 2 pm to 6 pm.

* The increase in temperature during 6 am to 10 pm = 40-37 = 3℃

* The decrease in temperature during 10 am to 2 pm = 40-38 = 2℃

The decrease in temperature during 2 pm to 6 pm = 38-35 = 3℃

* The temperature decreases more rapidly during 2 pm to 6 pm than 10 am to 2 pm.

* The temperature at 12 pm = 39℃ (not given in the record but we can interpret it from the graph).

* Ratio of total increase in temperature to total decrease in temperature during 6 am to 6 pm = 3/5

* Percentage decrease in temperature during 10 am to 2 pm = (2/40)×100 = 5%

* Net change in temperature during 6 am to 6 pm = -2℃

& so on…

## Linear Graph

Graph containing single unbroken line is called linear graph. In linear graph, x & y vary at constant rate. All data points on such graph are collinear.

 Linear Graph

🔹 In a line graph, every point on the graph (line) represents different value of x & y, i.e., for every different x there is different y. This is true for any point on the plane of the graph. Thus, every point on the plane of graph has unique value w.r.t. the origin. We will use this property to find the location (coordinates) of a point in a plane.