Chart and Graphics

Charts and Graphs Quiz Best MCQs

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These Online MCQs Charts and Graphs Quiz contain questions from different topics related to the graphical Presentation of data in statistics MCQs which include, Histogram, Frequency distribution (Relative frequency distribution, Cumulative Frequency distribution),  Bar chart, Pie chart, Line graph, scatter diagram, etc.

Charts and Graphs Quiz

MCQs Charts & Graphs 03MCQs Charts & Graphs 02MCQs Charts & Graphs 01
Online MCQs Charts and Graphs Quiz with Answers

This graph and chart multiple-choice questions (MCQ) test contains questions from different topics related to the graphical Presentation of data in statistics MCQs which include, Frequency distribution (Relative frequency distribution, Cumulative Frequency distribution), Bar graph, Pie chart, Line graph, scatter diagram, etc.

Graphs and charts are common methods to get a visual inspection of data. Graphs and charts are the graphical summaries of the data. Graphs represent diagrams of a mathematical or statistical function, while a chart is a graphical representation of the data. In the charts, the data is represented by symbols.

The most commonly used graphs and charts are bar charts, histograms, pie charts, and line graphs. Graphs are used to get quick ideas and decisions about phenomena under study. Generally, graphs and charts are used to get the distribution of data. However, different graphs and charts are used to get quite different information.

For example, line graphs are used to get ideas about changes over short/long periods of time. Bar graphs and their further types (cluster bar graph, stacked bar graph) are used to compare the differences among the groups. Pie charts are used to get the proportional contribution of each group about the whole.

Charts and Graphs Quiz

The important features of graphs and charts are (1) Title: the title of charts and graphs tells us what the subject of the chart or graph is, (2) Vertical Axis: the vertical axis tells us what is being measured in the chart and a graph, and (3) Horizontal Axis: the horizontal axis tells us the units of measurement represented.

There are various mathematical and statistical software that can be used to draw charts and graphs. For example, MS-Excel, Minitab, SPSS, SAS, STATA, Graph Maker, Matlab, Mathematica, R, Exlstat, Python, Maple, etc.

Note that

  • All graphs are charts, but not all charts are graphs.
  • Charts present information in a general way.
  • Graphs show the connections between pieces of data.
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Graphical Presentation of Data (2013)

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Getting expertise in the graphical presentation of data is important and also the major way to get insights about data.

Graphical Presentation of Data

A chart/ graph says more than twenty pages of prose, it is true when you are presenting and explaining data. The graph is a visual display of data in the form of continuous curves or discontinuous lines on graph paper. Many graphs just represent a summary of data that has been collected to support a particular theory, to understand data quickly in a visual way, by helping the audience, to make a comparison, to show a relationship, or to highlight a trend.

Usually, it is suggested that the graphical presentation of the data should be carefully looked at before proceeding with the formal statistical analysis. It is because the trend in the data can often be depicted by the use of charts and graphs.

A chart/ graph is a graphical presentation of data, in which the data is usually represented by symbols, such as bars in a bar chart, lines in a line chart, or slices in a pie chart. A chart/ graph can represent tabular numeric data, functions, or some kinds of qualitative structures.

Common Uses of Graphs

Graphical presentation of data is a pictorial way of representing relationships between various quantities, parameters, and variables. A graph summarizes how one quantity changes if another quantity that is related to it also changes.

  1. Graphs are useful for checking assumptions made about the data i.e. the probability distribution assumed.
  2. The graphs provide a useful subjective impression as to what the results of the formal analysis should be.
  3. Graphs often suggest the form of a statistical analysis to be carried out, particularly, the graph of model fitted to the data.
  4. Graphs give a visual representation of the data or the results of statistical analysis to the reader which are usually easily understandable and more attractive.
  5. item Some graphs are useful for checking the variability in the observation and outliers can be easily detected.
Graphical Presentation of Data

Important Points for Graphical Presentation of Data

  • Clearly label the axis with the names of the variable and units of measurement.
  • Keep the units along each axis uniform, regardless of the scales chosen for the axis.
  • Keep the diagram simple. Avoid any unnecessary details.
  • A clear and concise title should be chosen to make the graph meaningful.
  • If the data on different graphs are to be measured always use identical scales.
  • In the scatter plot, do not join up the dots. This makes it likely that you will see apparent patterns in any random scatter of points.
  • Use either grid rulings or tick marks on the axis to mark the graph divisions.
  • Use color, shading, or pattern to differentiate the different sections of the graphs such as lines, pieces of the pie, bars, etc.
  • In general start each axis from zero; if the graph is too large, indicate a break in the grid.

For further reading about the Graphical Presentation of data go to https://en.wikipedia.org/wiki/Chart

Graphical Presentation of Data in R Language

Stem and Leaf Plot: Exploratory Data Analysis

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Before performing any statistical calculation (even the simplest one), data should be tabulated or plotted especially if they are quantitative and are few (few observations) to visualize the shape of the distribution.

A stem and leaf plot summarizes the set of data measured on an interval scale in condensed form. Stem and leaf plots are often used in exploratory data analysis and help to illustrate the different features of the distribution of the observed data. A basic stem and leaf display contains two columns separated by a vertical line. The left side of the vertical line contains the stems while the right side contains the leaves. It is customary to sort the values within each stem from smallest to largest. In this statistical technique (to present a set of data), each numerical value is divided into two parts

  1. Leading Digit(s)
  2. Trailing Digit

Stem values are the leading digit(s) and leaves are the trailing digit. The stems are located along the vertical axis, and the leaf values are stacked against each other along the horizontal axis.

A stem and leaf display is similar to a frequency distribution with more information. It provides information about the observed data set’s symmetry, concentration, empty sets, and outliers. Organizing the data into a frequency distribution has the disadvantage of

  1. Lose of the exact identity of each value (individuality of observation vanishes)
  2. Did not know (sure) how the values within each class are distributed.

The advantage of the stem and leaf plot (display) over a frequency distribution is that we do not lose the identity (individuality) of each observation. Similarly, a stem and leaf plot is similar to a histogram but usually provides more information for a relatively small data set.

More than one data set can be compared by using multiple stem and leaf plots. Using a back-to-back stem and leaf plot we can compare the same characteristics into different groups.

The origin of the stem and leaf plot is associated with Tukey, J.W (1977).

Constructing a Stem and Leaf Plot

Let us have the following data set: 56, 65, 98, 82, 64, 71, 78, 77, 86, 95, 91, 59, 69, 70, 80, 92, 76, 82, 85, 91, 92, 99, 73 and want to draw the required graph of the given data.

First of all, it’s better to sort the data. The sorted data is 56, 59, 64, 65, 69, 70, 71, 73, 76, 77, 78, 80, 82, 82, 85, 86, 91, 91, 92, 92, 95, 98, 99.

Now the first digit is the stem and the second one is a leaf, i.e. stems are from 5 to 9 as data ranges from 56 to 99.

Draw a vertical line separating the stem from the leaf. Put stem values on the left side of the vertical line (bar) and leaf values on the right side of the vertical line.  Note that Each number is assigned to the graph (plot) by pairing the unit digit, or leaf, with the correct stem. The score 56 is plotted by placing the units digit  6, to the right of stem 5.

The stem and leaf plot of the above data would look like.

The decimal point is 1 digit(s) to the right of the |
Stem | Leaf
5      | 6 9
6      | 4 5 9
7      | 0 1 3 6 7 8
8      | 0 2 2 5 6
9      | 1 1 2 2 5 8 9

The stem and leaf plot looks like a histogram by rotating it anti-clockwise.

By adding columns of frequency and cumulative frequency in the stem and leaf plots we can find the median of the data.

stem and Leaft Plot
Stem and Leaf Plot

Reference

Histogram Graph: Useful Graphical Representation of Data

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A histogram is very similar to the bar chart for a frequency distribution based on quantitative data showing the distribution of qualitative data. It is a useful graphical representation of data that helps to visualize the distribution of data.

Important Points to Draw a Histogram Graph

The histogram is constructed from the grouped data by taking the class boundaries (not class limits) along the x-axis and the corresponding frequencies along the y-axis. For ungrouped data, we have to form the grouped frequency distribution before making a histogram. It consists of a set of bars (like a bar chart) but these bars are adjacent to each other and the height of the bars is proportional to the frequency associated with respective classes.

The area of each rectangle represented the respective class frequencies. When the class intervals are equal, the rectangles all have the same width and their heights directly represent the class frequencies. For the case in which class intervals are not all equal, the height of the rectangle (bar) over an unequal class interval, is to be adjusted because it is area and not the height that measures frequency. This means that the height of a rectangle must be proportionally decreased if the length of the corresponding class interval increases.

For example, if the length of a class interval becomes double, then the height of the rectangle is to be halved so that area, being the fundamental property of the rectangle of the histogram remains unchanged. This sort of rescaling is necessary to observe the correct pattern of distribution.

Important Features of Histogram

The important feature of the Histogram graph is that there is no gap (space) between the vertical bars because the variable plotted on the horizontal axis is quantitative and the variable is from the measure of scale either interval or ratio. Thus, it provides an easily interpreted visual representation of a frequency distribution. Note that class midpoints are used as labels for the classes.

It allows us to analyze extremely large datasets by reducing them to a single graphical representation which is used to show primary, secondary, and tertiary peaks in data, and also helps us by giving a visual representation of the statistical significance of those peaks.

Alternative of Histogram

An alternative to the histogram is kernel density estimation, which uses a kernel to smooth samples. This will construct a smooth probability density function, which will, in general, more accurately reflect the underlying variable.

Histograms for Continuous Grouped Data

To draw a histogram graph from the continuous grouped frequency distribution, the following steps are taken.

  1. Mark the class boundaries of the classes along the x-axis.
  2. Mark frequencies along the y-axis.
  3. Draw a rectangle for each class such that the height of each rectangle is proportional to the frequency corresponding to that class. This is the case when classes are of equal width as they often are.
  4. If the classes are of unequal width, then the area instead of the height of each rectangle is proportional to the frequency corresponding to that class, and the height of each rectangle is obtained by dividing the frequency of the class by the width of that class.

It may be noted that the area under a histogram graph can be calculated by adding up the areas of all the rectangles that constitute the histogram. The area of one rectangle is obtained by the multiplication of the width of the class by the corresponding frequency i.e.

Area of a single rectangle = width of the class x frequency of the class

Histogram for Discrete Data

Bar graphs are usually drawn for discrete and categorical data but there are some situations where there is a need to make an approximation, the histograms may be constructed. To construct a histogram graph for discrete grouped data, the following steps are taken:

  1. Mark possible values on the x-axis.
  2. Mark frequencies along the y-axis.
  3. Draw a rectangle centered on each value with equal width on each side possibly 0.5 to either side of the value.
Histogram graph

The advantages of the histograms as compared to the unprocessed data are:

  1. It gives a range of data.
  2. It gives the location of the data.
  3. it gives a clue about the skewness of the data.
  4. It gives information about the out-of-control situation.
  5. Histograms are density estimates (give a good impression of the distribution of data.
  6. Can be compared to the normal curve.

The disadvantages are:

  • Exact values cannot be read from histogram graph because data is grouped into categories and individuality of data vanishes in grouped data.
  • It is more difficult to compare two data sets.
  • It is used only for the continuous data set.

FAQs about Histogram

  1. What is a histogram graph?
  2. What is the difference between a bar chart and a histogram?
  3. What are the important features of histograms?
  4. What are the advantages and disadvantages of histogram graphs?
  5. How one can draw a histogram for a discrete data set?
  6. How one can draw a histogram for a continuous data set?

Graphical Representation of Data, Data Visualization/ Graphics in R