Types of Graph


 

Types of Graph

 
There are different types of graphs available in statistics, some of the common types of graphs are as below





Lets discuss one by one
  1. Ogives
  2. Histogram
  3. Bar Chart
  4. Pie Chart
  5. Line Chart
  6. Scatter Plot
  7. Measures of Dispersion
  8. Normal Distribution
  9. Range
  10. Box and Whisker Plot
  11. Percentile
  12. Variance and Standard Deviation

1. Ogives: 

An ogive is a graph of the cumulative relative frequency from a relative frequency distribution. 

  • Ogives are sometime shown in the same graph as a relative frequency histogram.

  • Example: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 




Add a cumulative relative frequency column:




2. Histogram 

A histogram is a display of statistical information that uses rectangles to show the frequency of data items in successive numerical intervals of equal size. 

  • The classes or intervals are shown on the horizontal axis while the frequency is measured on the vertical axis.
  • Bars of the appropriate heights can be used to represent the number of observations within each class such a graph is called a histogram .
  • Example: Data: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58



Histogram in Excel


  • Bin is also known as class interval 
  • In Excel, we can decide whether to give a bin range or not 
  • Excel automatically takes the bin range once data is provided


3. Bar Chart

A bar chart or bar graph is a chart or graph that presents categorical data with rectangular bars with heights or lengths proportional to the values that they represent.

Bar charts is often used for qualitative (category) data.. Example:


4. Pie Chart 

A pie chart is a circular statistical graphic which is divided into slices to illustrate numerical proportion. 

  • In a pie chart, the arc length of each slice (and consequently its central angle and area), is proportional to the quantity it represents. 
  • Size of pie slice shows the frequency or percentage for each category.
  • Example:

Current Investment Portfolio



Steps to draw a bar chart and pie chart in excel
  1. Select the data.
  2. Go to insert and click on recommended chart.
  3. Go to all chart and select the required chart for bar chart or pie chart 

5. Line Chart

A line chart or line graph is a type of chart which displays information as a series of data points called 'markers' connected by straight line segments.

  • Line charts show values of one variable vs. time.
  • Time is traditionally shown on the horizontal axis.
                                       

                                         

6. Scatter Plot

A scatter plot (also called a scatterplot, scatter graph, scatter chart, scattergram, or scatter diagram) is a type of plot or mathematical diagram using to display values for typically two variables for a set of data.

  • Scatter Diagrams show points for bi-variate data. One variable is measured on the vertical axis and the other variable is measured on the horizontal axis. 
  • Purpose: Scatter plots shows the relationship between two variables.

7. Measures of Dispersion

The measure of dispersion indicates the scattering of data. It explains the disparity of data from one another, delivering a precise view of the distribution of data.

  • Dispersion is the extent to which a distribution is stretched or squeezed. 
  • Summary statistics can also be used to understand variation or dispersion in the data
  • There are 4 types in Measures of Dispersion
      1. Range
      2. Mean Deviation
      3. Variance
      4. Standard Deviation

 

8. Normal Distribution (Bell Shaped Curve)

Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. In graph form, normal distribution will appear as a bell shaped curve.

  • A normal distribution is the distribution in which most values cluster in the middle of the range and the rest taper off symmetrically toward either extreme.
  • Height is one simple example of something that follows a normal distribution pattern: Most people are of average height, the number of people that are taller and shorter than average are fairly equal and a very small (and still roughly equivalent) number of people are either extremely tall or extremely short.


9. Range

It is the difference between a highest and a lowest observation.
    1. Range = Highest observation - lowest observation
    2. Example: In {2, 3, 4, 6, 9, 3, 7, 16, 21 } the lowest value is 2, and the highest is 21 Range: 21 – 2 = 19
    3. The range can sometimes be misleading when there are extremely high or low values.
    4. Example: 


10. Box and Whisker Plot

Box and Whisker Plot is a convenient way of visually displaying the data distribution through their quartiles. The lines extending parallel from the boxes are known as the “whiskers”, which are used to indicate variability outside the upper and lower quartiles.

  • Box-and-whisker plots are a handy way to display data broken into four quartiles, each with an equal number of data values. It shows where the middle of the data lies. It's a nice plot to use when analyzing how your data is skewed.
  • The median is the middle value of the data where half of the points are above and half are below this value.
  • The first quartile represents the point where 25% of the data is below it.
  • The third quartile represents the point where 75% of the data is below it.
  • The whisker extends up to the highest value of upper limit and down to the lowest value of the lower limit.
  • The lowest point of the lower whisker is called the lower limit. It equals Q1 – 1.5 * (Q3-Q1 or interquartile range).
  • The highest point of the upper whisker is the called the upper limit. It equals Q3 + 1.5 * (Q3-Q1).
  • Outliers are points that fall outside the limits of the whiskers.
  • The interquartile is represented by the distance between Q1 and Q3.



11. Percentile

A percentile (or a centile) is a measure used in statistics indicating the value below which a given percentage of observations in a group of observations fall.

  • For example, the 20th percentile is the value (or score) below which 20% of the observations may be found.
  • The p'th percentile in an ordered array of n values is the value in i'th position,



Example: Find the 60th percentile in an ordered array of 19 values


11. Variance and Standard Deviation 


Variance

  • Variance is a measurement of the spread between numbers in a data set.
  • It measures how far each number in the set is from the mean.
  • If the data is a Sample (a selection taken from a bigger Population), then the calculation changes! When you have "N" data values:

The Population: divide by N 
A Sample: divide by N-1




To calculate the variance follow these steps:
  1. Work out the Mean (Simple average of the numbers)
  2. Then for each number: subtract the Mean and square the result (the squared difference).
  3. Then work out the average of those squared differences.
Example 
 You and your friends have just measured the heights of your dogs (in millimeters):

The heights (at the shoulders) are: 600mm, 470mm, 170mm, 430mm and 300mm.

First step is to find the Mean:
Answer:

so the mean (average) height is 394 mm. Let's plot this on the chart: 


Now we calculate each dog's difference from the Mean:

To calculate the Variance, take each difference, square it, and then average the result:

The variance is 21,704



Standard Deviation
  • Standard deviation is a measure of the dispersion of a set of data from its mean.
  • Standard deviation s (or σ) is just the square root of variance s2 (or σ 2).
  • When we calculate the standard deviation of normal distribution we find that (generally): 

  • Lets continue example, (where the variance was 21704)
  • The Standard Deviation is just the square root of Variance, so: Standard Deviation: σ = √21,704 = 147.32... = 147 (to the nearest mm)
  • We can show which heights are within one Standard Deviation (147mm) of the Mean (394mm): 


So, using the Standard Deviation we have a "standard" way of knowing what is normal, and what is extra large or extra small. 
Rottweiler's are tall dogs and Dachshunds are a bit short.

Lets understand statistics formule with the business problem

Business Problem:

A firm is starting a delivery service for a new client between 2 points. Since it is a new client, the firm wants to send more consistent delivery boy to deliver the product.

Delivery boy 1 (Time in minutes) – 12,13,17,21,24, 24, 26,27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46,53,60

Delivery boy 2 (Time in minutes)- 34, 14, 31, 59, 11, 50, 27, 33, 53, 34, 13, 13, 42, 29, 33, 42, 34, 33, 44, 21 

The average time taken by both the delivery boys is same i.e 32.5 minutes How can the firm arrive on a conclusion?

Solution 

  • Excel Formula =stdev(data)
  • Standard deviation of the delivery time taken by delivery boy 1: 12.89
  • Standard deviation of the delivery time taken by delivery boy 2: 13.55

From the above observations, we can conclude that Delivery boy 1 is more consistent than delivery boy 2. Hence , firm should send delivery boy 1




Author:  Mohit T (Algae Services)

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