# Chart and Graphics

## MCQs on Graphs and Charts 3

This Online quiz about MCQs on Graphs and Charts contains questions from different topics related to the graphical Presentation of data in statistics MCQs on graphs and charts which include, Histogram, Frequency distribution (Relative frequency distribution, Cumulative Frequency distribution),  Bar chart, Pie chart, Line graph, scatter diagram, etc.

Let us start the Third online MCQ on Graphs and charts.

MCQs about Statistical Charts and Graphs

1. A pictorial diagram of frequency distribution is denoted

2. In a Pie chart, usually, the arrangement of the sectors is:

3. Which of the following types of diagrams can be used to find out the relationship between two variables?

4. A circle in which sectors represent various quantities is called

5. A frequency curve touches x-axis

6. Component bar charts are used when data is divided into:

7. A graphical device used for enumerating sample points in a multiple-step experiment is a

8. The line chart of the medical/ health data shows

9. A(n) ________ is a graphical representation in which the sample space is represented by a rectangle and events are represented as circles

10. Low Birth Weight (LBW) data of a Hospital is best shown by

11. For geographically base data, the bars are used:

12. A histogram is

13. A graphical method of representing the sample points of a multiple-step experiment is

14. The frequency polygon is a closed diagram of

15. In a Pie chart, the angels for each sector are calculated by the formula

16. Which of the following is an example of compressed data:

17. A Histogram containing a set of

18. If the frequency curve has a longer tail to the left, the distribution is

19. Frequency curve is

20. Decumulative frequency is presented by

Graphical & charting representations are common methods to get a visual inspection of data. The graphs 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 graphical summaries of the data 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 each group’s proportional contribution to the whole.

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.

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

### MCQs on Graphs and Charts

• A graphical device used for enumerating sample points in a multiple-step experiment is a
• A graphical method of representing the sample points of a multiple-step experiment is
• A(n) __ is a graphical representation in which the sample space is represented by a rectangle and events are represented as circles
• A Histogram containing a set of
• Which of the following is an example of compressed data:
• For geographically base data, the bars are used:
• Decumulative frequency is presented by
• The frequency polygon is a closed diagram of
• A frequency curve touches the x-axis
• Frequency curve is
• Component bar charts are used when data is divided into:
• In a Pie chart, usually, the arrangement of the sectors is:
• In a Pie chart, the angels for each sector are calculated by the formula
• A circle in which sectors represent various quantities is called
• If the frequency curve has a longer tail to the left, the distribution is
• A histogram is
• Low Birth Weight (LBW) data of a Hospital is best shown by
• A pictorial diagram of frequency distribution is denoted
• Which of the following types of diagrams can be used to find out the relationship between two variables?
• The line chart of the medical/ health data shows

Online MCQs Test with Website

## Graphical Presentation of Data

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

### 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

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 is a way of summarizing 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 of the vertical line 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

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 symmetry, concentration, empty sets, and outliers of the observed data set. 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.

Reference

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