Data representation is an important and interesting aspect of Descriptive Statistics. Many techniques and tools are used to represent data in a clearly understandable way.

We learn many types of graphs like Line-Plots, Bar Graphs, Histograms and Stem and Leaf Plot to name a few. Line Plot is the simplest and easiest of these types of Data Presentation. We are all quite comfortable using the number line. With the minimal skill of counting numbers, Line Plots can be made to give impressive and useful data charts.

## Line Plot

Line Plot is a diagrammatic representation of data displayed on a number line. For any Statistical Graph, the data has to be tallied and organized in some form. A frequency table is used to tally or count the number of different categories and find their frequencies. Line Plot provides a method to tally and organize data direct on the chart when the categories being tallied are numbers. For this matter, Line Plots can also be understood as data tallied on a number line.

A line Plot uses X marks above a number line to show the frequencies. The X marks can also be replaced with a dot or some picture, motif or design related to the data set.
The Line Plot is also sometimes called a Dot Plot.Line Plots are not only a useful data display, but can also be used for data analysis. Each data value is clearly represented on a Line Plot. A quick observation of a Line Plot gives the range and mode of the data set direct. As the data values are placed in numerical order, the median can be easily found using a Line Plot. Line Plots clearly show clusters, gaps and outliers in data sets.

## Line Plot Graphs

Let us learn how to make a Line Plot and use it find the Range, mode and median of a data set.
The following frequency table shows the time spent on preparation on the eve of a Math Exam.

The same tallies can be made using X marks on the number line corresponding to the hours studied.

We can observe the following features on the line plot shown above.
1. The number line shows the different times spent on studying in minutes.
2. The X mark is used as a tally for counting the frequencies and the number of x marks above different numbers show the corresponding frequencies.
3. The number line need not start at zero. But should include all the values within the range even if no tally x's shown above them.
4. The minimum of the data values is the value above which the first x mark appears and the maximum is the value above which the last of the X marks appear. It can be seen, the minimum and maximum values are 30 and 70.
5. The Range of the data values = Maximum value - Minimum Value = 70 -30 = 40.
6. 9 students have studied 50 minutes prior to exam, which is the highest frequency that can be seen direct on the plot. Hence the mode of the data set is 50 minutes.
7. Crossing one X mark on either end we can arrive at the median value at the 2nd X Mark above 50. Hence the median of the data set = 50.
8. The mean of the data set cannot be directly found from a Line Plot. The value of the mean calculated using the formula $\frac{\sum fx}{N}$ = 48.
9. The time studied appear to be clustered between 40 minutes and 55 minutes.
10. There is no frequency for the data value 65 minutes which forms a gap.
11. One student has spent much more time than the rest, while one has studied much less. The values 70 and 30 are hence outliers.

## Line Plot Examples

### Solved Examples

Question 1: The following data shows the number of children in fifty families in a neighborhood. Tally the data on a line Plot and find the range, median and mode of the data set.

Solution:

The Line Plot for the data is shown below:

The minimum and maximum data values are 1 and 5. Hence the range of the data set = 5 - 0 = 5.
The data value 2 has maximum number of frequencies = 15. Hence the mode of the data = 2.

After crossing equal number X's on either side, the remaining two middle X's stand on the data value 2.
Hence the median of the data set = 2.

Question 2: The following Line Plot displays the Quiz scores in a class of 27 students. Identify the clusters,
gaps and outliers if present from the graph.

Solution:

The Quiz scores seems to be concentrated between 6 and 8. Hence the three scores 6,7 and 8 form a cluster.

No frequencies are seen for scores 4 and 5. Thus the scores 4 and 5 form a gap. We need not consider the possible scores 0,1 and 2 as the minimum value shown on the graph is 3. A lone student has scored only 3,thus making this value an outlier.