## Types of Graphs and Charts

The graphical demonstration of statistical data in a chart is normally specified as statistical graph chart. There are many kinds of graphs and charts which are used to indicate a set of data. The data is either unremitting or separate. These graphs are very helpful to recognize the statistical data.

### Types of Graphs and their Uses

There are different kinds of graphical charts based on statistics as follows:

Line graphsPie chartsBar graphScatter plotStem and plotHistogramFrequency polygonFrequency curveCumulative frequency or ogives

Let us study the graphs and their uses in detail.

__Line Graphs__

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A line graph is a diagram that shows a line joining several points, or a line that shows the relationship between the points. A line graph can be taken as xy plane, where there will be an independent variable and a dependent variable and it specifies how the two variables are related to each other and vary with respect to one another. Mostly, the independent variable is taken on the x-axis while the dependent variable on the y-axis.

### Solved Example

**Question:** The table given below shows the weights of a set of people -

**Month**
**Weight (kg)**1383
415
437
499
5111
54

**Solution:**
The data as per given in the table above has been summarized in the form of a line graph below.

## Pie Charts

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A pie chart can be taken as a circular graph which is divided into different disjoint pieces, each displaying the size of some related information. The highlight of this graph is that it represents a whole and each part represents a percentage of the whole. Hence, pie charts are best used with respect to categorical data which helps one understand what percentage each of these category constitutes. It also has a good visual treat and the percentage value of each section is instantly known.

### Solved Example

**Question:** The following table shows the expenses of a nuclear family for a month for some day to day items:

**Expense**
**Money//$**Mortgage
400Food
120Dress
80
**Solution:**
The total monthly expenditure= 400$$ + 120$$ + 80$$ = 600$$

To draw a pie chart, first lets form a pie chart using the relevant formula.

**Subject**
**Ratio**Mortgage400600400600 ×× 360 = 240Food120600120600 ×× 360 = 72Dress8060080600 ×× 360 = 48
It can be seen that the total of the ratios equals 240 + 72 + 48 = 360

So we get pie diagram:

## Bar Graph

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Bar graph is drawn on an x-y graph and it has labelled horizontal or vertical bars that show different values. The size, length and color of the bars represent different values. Bar graph is very useful for non continuous data and it helps in comparing or contrasting the size of the different categories of the data provided.

Lets take an example of the bar diagram and compare the pass percentage of a school during the year 2000, 2001 and 2002.

__Scatter Plot__

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A scatter plot or scatter graph is a type of graph which is drawn in Cartesian coordinate to visually represent the values for two variables for a set of data. It is a graphical representation that shows how one variable is affected by the other. The data is presented in the form of collection of points, each of which has one value of a variable positioned on the horizontal or x-axis, also called explanatory variable and the value of the other variable positioned on the vertical or y-axis, also called response variable.

### Solved Example

**Question:** Consider the table that gives the data which shows the relation between height and size of shoes for a set of people. Using the data plot a graph.

**Height(in inches)**
**Shoe size**
60
3
61
362
463
464
565
566
667
668
7

**Solution:**
Using the data given in above table we can plot the graph

Each data point denoted by a small circle in the graph represents the shoe size at a particular height on two variables. Note that these data are not random, but rather seem to show a general tendency for the scores on x-axis to increase as the hours of y axis increase.

## Stem and Leaf Plot

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Stem and leaf plot also called as **stem plot** are connected with quantitative data such that it helps in
Displaying shapes of the distributions,Organize numbers andSet it as comprehensible as __possible.It__ is a descriptive technique which gives more emphases on the data provided. It concludes more about the shape of a set of data and provides better view about each of the data. The data is arranged by “place value”. In Stem plots each data is taken and divided such that, they form two separate parts, a **stem** and a **leaf**. A stem is usually the first digit of the number in the data, and a leaf is the last digit of the number in the data. We write the stems in a vertical column and draw a vertical line to the right of the column. And hence we can write the leaves in the row to the right side of the corresponding stem.

In general the following steps have to be followed while forming a stem and leaf plot.

First the numbers has to be arranged in ascending order that is from smaller to bigger number. The digits at large place form the stem and the ones at the smallest place forms the leaf The leaf is placed to the right of the stem separated by a division or line. For each stem digit, there may be a different or same leaf digit, so it can be placed horizontally in the same row where the stem is kept.

### Solved Example

**Question:** Consider the following set of numbers

12, 16, 32, 56, 24, 37, 92, 86, 54, 11, 96, 75, 38, 97, 57, 43, 61, 83, 93, 47, 99, 87.
**Solution:**
**Step 1:**
First the numbers has to be arranged in ascending order that is from smaller to bigger number
11, 12, 16, 24, 32, 37, 38, 43, 47, 54, 56, 57, 61, 75, 83, 86, 89, 92, 93, 96, 97, 99.

**Step 2**:
The digits at large place form the **stem** and the ones at the smallest place forms the **leaf**.
Stem will contain the tens digit, as the numbers are between 11 and 99. So place them vertically in order from smaller to bigger. Here, there is no need to repeat the digit.

**Step 3:**Working from left to right, place the unit digits, in the leave place in front of the corresponding row. Here there is 11, 12, 16 So we write

**Step 4:**
In the same way, the __whole numbers__ are plotted.

**Step 5:**
At last, remember to create a legend (key) for the figure drawn. It will help in reading the values of the number in the plot.

=> Legend 2|4 is 24 5|7 is 57 Hence the diagram is formed.

__Histogram__

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Histogram is the most accurate graph that represents a frequency distribution. In the histogram the scores are spread uniformly over the entire class interval. The class intervals are plotted on the x-axis and the frequencies on the y-axis. Each interval is represented by a separate rectangle.

The area of each rectangle is proportional to the number of measures within the class- interval. The entire histogram is proportional to the statistical data set.

Lets consider a data table and lets try to draw a histogram of it.

**Class interval**
**frequency**
0-10110-20
320-30
630-40
440-50
2
To plot this take the class limits on the x-axis and the frequency on the y-axis. On the x-axis, the scale can be 10 units whereas on the y-axis the scale can be 1 unit. Hence, we get

__→ Read More__## Frequency Polygon

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The frequency polygon has most of the properties of a histogram, with an extra feature. Here the mid point of each class of the x-axis is marked. Then the midpoints and the frequencies are taken as the plotting point. These points are connected using line segments. We also complete the graph, that is, it's closed by joining to the x-axis. Frequency polygon gives a less accurate representation of the distribution, than a histogram, as it represents the frequency of each class by a single point not by the whole class interval.

Lets consider a data table and lets try to draw an ogive of it.

### Solved Example

**Question:** Draw an graph by using data given below:

**Class intervalfrequency**0-10
110-20
320-30
630-40
440-50
2
**Solution:**
**Step 1:**
First we need the mid point of the class interval.

**Class interval**
**midpoint**
**frequency**0-10
5110-20
14320-30
25630-40
35440-50
452
**Step 2:**
**T**he frequency polygon obtained is

## Frequency Curve

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The frequency polygon consists of sharp turns, and ups and downs which are not in conformity with actual conditions. To remove these sharp features of a polygon, it becomes necessary to smooth it. No definite rule for smoothing the polygon can be laid down. It should be understood very clearly that the curve does not, in any way, sharply deviate from the polygon. In order to draw a satisfactory frequency curve, first of all, we need to draw a frequency histogram, then the frequency polygon and ultimately the frequency curve.

__Cumulative Frequency__

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Cumulative frequency is a graph plotting cumulative frequencies on the y-axis and class scores on the x-axis. The difference between frequency curve and an ogive is that in the later we plot the cumulative frequency on the y-axis rather than plotting the individual frequencies. The advantage of an ogive is that it enables median, quartiles, etc to be studied from the graph.

### Solved Example

**Question:** Consider a data table and lets try to draw a ogive of it.

**Class interval**
**frequency**
0-10
110-20
320-30
630-40
440-50
2

**Solution:**
**Step 1:**
From the table given, lets make the cumulative __frequency table__ for both less than and greater than ogive.
**Less than ogive**

**Upper limit**
**Cumulative frequency**10
1201 + 3 = 430
4 + 6 = 1040
10 + 4 = 1450
14 + 2 = 16
The curve corresponding to this is

**Step 2:**

**Greater than ogive**When the

__lower limit__is plotted against cumulative frequencies, we get

**greater than ogive**.

**Lower limit**
**Cumulative frequency**
01610
16 - 1 = 1520
15 - 3 = 1230
12 - 6 = 640
6 - 4 = 2
The curve corresponding to this is

## Graph Problems

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Given below are some of the examples on graphs.

### Solved Examples

**Question 1:**

Draw the graph for given data.

ItemRiceChocolateMilkDrinksQuality45%25%90%65%
**Solution:**

Following is the pie Chart of the given data-

**Question 2:**

Draw the line graph for given data.

Time3.304.004.305.00Frequency2.785.761.95.76
**Solution:**

Following is the line graph representing the given data

**Question 3:** Draw the graph of scatter plot.Hours Of Study2 hours3 hours5 hours7 hoursScores50758595
**Solution:**

Following is the __plot graph__ representing the given data

source : __https://math.tutorvista.com/statistics/types-of-graph.html__

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