Real Life Stat Examples

¶ … real life example, we would compare the quarterly sales over 4 years. For this the following values would be made Line Graphs Pie Charts Colum Chart Scatter Charts Misleading charts and graphs Graphs and charts are tools for statistical analysis of data and information. Graphs and charts help identify and illustrate in a meaningful manner, the trends and details of the data.

Sometimes, data or information involves very large volume of data and would be too cumbersome to get them printed or to make non-technical people understand the trends and details of the data. On such occasions, using graphs and charts to represent the data in a simple and understandable manner is useful (Bhaduri and Ghosh, 2014). Therefore it can be said that a graph or a chart shows thousands of information in a picture and help convey information quickly and easily to the user.

The salient features of the data are highlighted by graphs and charts. Often relationships between various sets of data cannot easily be related. Graphs and charts helps relate and compare such data sets. Graphs and charts therefore help to convey to the users comparisons and relationships, distribution, trends, composition, flow and/or process and location that are sought to be obtained from a data set. Easy-to-understand formats that clearly and effectively communicate important points is enabled by graphs and charts by the condensation of large amounts of information.

The selection of the type of chart or graph to be used, the purpose of the graph or chart needs to be considered in terms of what one wants to present. For example, one could choose between expressing certain data set in the form of frequencies, percentages or categories. Also the type of data that one is working with needs to be considered while selecting the chart or graph type.

While categorical data are grouped into non-overlapping categories such as grade, race, and yes or no responses, this can be represented by bar graphs, line graphs and pie charts. On the other hand continuous data are measured on a scale or continuum like such as weight or test scores which can be best represented through tools like histograms (Dehmer and Emmert-Streib, n.d.). In this question we would discuss the types of charts and graphs that can be used for quantitative analysis.

There are also several types of quantitative data such as: Discrete Data -- this is data that has distinct values or observations like 5 customers, 17 points, 12 steps etc. Continuous Data -- this type of data is represents any value or observation within a finite or infinite interval like conversion rate, visits, page views, bounce rate, height, weight etc. (Forsyth, 2013). Quantitative data can be summarized through mean, median, mode, standard deviation etc. And for this column chart, bar chart, line chart, Histogram etc. can be used.

In this question we would look into the usefulness of bar and line graphs and pie charts, column charts and scatter charts for analysis of quantitative data. Types of Graph Bar Graphs Direct comparison of two or more sets of data is done by the use of bra graphs. This is used when the number of time intervals is small and when there is time series data. Such graphs generally tend to have 0 as the baseline if all values are positive integers.

Zero would be the midpoint of the scale in cases where the values include both positive and negative integers such as in the case of graphing differences in means. However the scale ranges should not vary between graphs and should be standardized whenever possible. It is best not to use 3-D features in a bar graph as such graphs are complex in nature and makes them ineffective in conveying results to most audiences. It also leads to distortion of data.

Both horizontal and vertical bars can be included in bar graphs. But horizontal bar charts are rarely used to portray time series. In order to have the maximum effect of comparison of data and information in a bar graph, the columns should be sorted in some systematic order, most often according to size of value, to have visually effective schema. The standardized grade scale is used to order findings by a particular category.

Without the presence of a standard base line, stacked bar graphs that are composed of one or more segmented bars where each one of the segment represents the relative share of a total category, are not very effective in conveying data and for comparison especially in among the second, third or subsequent segments (Hsin-Yi Tsai, Yu-Lun Huang and Wagner, 2009).

It is preferable to create a bar graph that groups these values together, side by side when the graphing data from two or more different series, or different classes within the same series. Taking a real life example, we would compare the quarterly sales over 4 years. For this the following values would be made: The Revenue in dollars would be placed along one axis. The time i.e. quarter number, would be plotted along another axis. There are four categories: Q1, Q2, Q3 and Q4.

Each category will have 4 columns for years say 2006 through 2009 The data for the graph would be: 2011 2012 2013 2014 Q1 25 58 45 65 Q2 89 Q3 75 89 83 90 Q4 The resultant Bar graph would be as follows: Line Graphs Most often time series data is displayed by line graphs. Line graphs are more effective in presenting five or more data points when in comparison to bar graphs but do not turn out to be much effective in cases where the period of time is less and there is less emphasis on the identification of the differences.

For plotting time series online graphs, the categories should be placed on the x-axis or the horizontal axis such as the week, months, years -- depending on the data and the frequencies of data that is to be measured on the y axis or the vertical axis. An example of a line graph can be had for representing the population trend of a country over a period of 11 years.

In this graph we would plot the time in years along the X- axis and the total population of the country would be plotted along the Y-axis. There would a large number of data points or categories. A line chart is chosen to represent the above mentioned data as the number of data points is very high and a column or bar chart will look pretty cluttered and would not be able to clearly identify a trend or even fit on a computer screen or an average page.

The attempt in using the line graph is to show the trend and not to show the maximum or the minimum population. The aim is to show the rate of population growth or decline or change of population which would be denoted by the steepness of the graph line instead of the actual population. Therefore to visualize trend-based data, a line chart is best suited (Hudak and Duplacey, 2008).

The data to be presented on a line chart are as below: Year (to be plotted on X-axis) Population (in millions) to be plotted on y-axis 2004 75 2005 80 2006 83 2007 78 2008 90 2009 92 2010 2011 2012 2013 2014 The line graph for the above data is represented a below. Here the blue line represents the change in population in a country over a period of 11 years. A user can easily get an idea about how the population of a country has changed over the 11-year period without actually requiring to know the exact population of the country at any year.

Graphs that have more than four or five lines tend is often confusing to decipher by the user unless the lines are well separated. In such cases it is the norm that, different line styles like solid line, dashed line, etc. And different colors and/or plotting symbols like asterisks, circles, etc. are used to separately identify the lines representing various data in a single graph for comparison.

If we add more values to the table above to denote the male and female population in every year of the 11-year period, the table would look as below: Year Population (in millions) Male (in millions) Female (in millions) 2004 75 35 40 2005 80 38 42 2006 83 38 45 2007 78 33 45 2008 90 42 48 2009 92 43 49 2010 47 53 2011 49 56 2012 52 58 2013 55 61 2014 57 62 Types of charts In this section we would discuss the three types of charts that can be used for evaluation and representation of quantitative data. Pie Charts Though pie charts are good to view and easy to understand, the generally have limited utility.

The charts are used to show parts of a whole where the whole is considered to be 100% and all the parts add up together to make 100. While pie charts do not make small differences apparent, they are able to emphasize general findings. Generally it is advised that the pie charts should not consist of more than five or six slices and should be used to represent categorical data with a relatively small number of values (Hudak and Duplacey, 2008).

As with bar graphs, pie charts should avoid the use of 3-D features or break out of the pieces as such graphs makes it difficult to compare the relative size of the slices. The category labels should always be included in pie charts so that users can relate a slice with the category that it represents. It is also advised that the category labels should be placed directly on the pie slices for clarity and easy comprehension.

For better understanding of the pie charts, value labels should be included in the charts that indicate the percentage of the pie represented by a given slice. To differentiate various sizes of pie charts different colors for different categories is easier to identify and differentiate. Pie graphs are best suited to represent and compare just one category of data and should not be used to represent more than one category for clarity and easy understanding (Schmuller, 2013).

For practical application of a pie chart we would represent the percentage composition of the types of vehicles that ply in a city on an average day. Category % of total vehicle Cars 32 Bikes 28 Lorry 15 Three wheelers 5 Bicycles 8 Walkers 12 A pie chart representing this data would look as below: Experts of statistics advise that pie charts should essentially be used when there are no more than 6 categories and when there is this one category that clearly has values more than the rest and it is necessary to highlight that category.

Pie charts are also useful in cases where two or more categories have almost the same values and for cases where there is need to sum up a couple or more categories and then compare them to another sum. Colum Chart Colum chart can be used to plot data that is arranged in columns or rows on a worksheet. Data changes over a period of time or for illustrating comparisons among items are best represented by Colum charts.

Categories are placed along the horizontal axis and values along the vertical axis in a Colum chart. Colum charts can be of various forms like the clustered column and clustered column in 3-D format. Values in 2-D vertical rectangles are displayed by clustered Colum charts and are useful for comparing values across categories. However a third value axis known as the depth axis is not used in a 3-D clustered column chart display which displays the data by using a 3-D perspective only.

The clustered Colum chart can be used in case of categories that represent varying ranges of values like item counts and for specific scale arrangements like a Likert scale with entries, such as strongly agree, agree, neutral, disagree, strongly disagree. This type of chart can also be useful for representation of categories when the names are not in any specific order like item names, geographic names or the names of people.

The stacked column and stacked column in 3-D chart show the relationship of individual items to the whole and is used to compare the contribution of each value to a total across categories. As is the case with clustered Colum charts, a third value axis or the depth axis is not used. This form of chart is useful for a large number of data and in cases where there is need to emphasize the total despite the presence of multiple data series (Schmuller, 2013).

We would show how a stacked column chart can be used to indicate the break-up of the visitors to a tourist site according to the duration of stay at the site. In this chart, the number of visitors is broken down as per the time they spend on the tourist site.

The above mentioned statistics is also compared through a stacked column chart depending on the day of the week that the visitors visit and hence the number of visitors by duration would in turn be broken down by the day of the week. The chart would also essential display the total number of visitors to the site on every day.

A stacked column chart would be used as such a chart would enable the visualization of the above data according to the break-up of visits by duration and as well as show the whole using the same data plot. This chart form is best used for data that has a limited number of categories -- five or seven.

From the above chart it is clear that the trend of the composition of visitors defined for each day and each time of the day and also gives an idea about the exact quantitative values of the number of people visiting the tourist site every day. This chart form therefore compares and composes data together in one chart form. Hence this chart is important to many analysts.

Scatter Charts In this form of chart, the data can be plotted in a xy or scatter chart when such data is arranged in columns and rows on a worksheet. The relationships among the numeric values in several data series is shown in scatter charts as well as enable the plotting of two groups of numbers as one series of xy coordinates.

There are two value axes in a scatter chart which plots one set of numeric data along the horizontal axis or the x-axis and another set of numerical data along the vertical axis or the y-axis. The result of the data along the two axis are displayed in.