In Descriptive Statistics, after data collection has taken place, it is then displayed and presented in various ways so as to make informed inferences. Reading all the data can be very intimidating. Hence, the data is depicted in the form of visually arresting tables and graphs to make them more comprehensible in interpreting the measurements. Research reports along with newspapers are magazines often post graphs to depict fact after an observation. These Graphs act a toll and aid us in understanding the sample and population distribution. There are various types of graphs that are used to summarize and depict the data of a sample such as : Histogram, bar graphs, steam-and-leaf ploy, pie chart, box plot and frequency polygon. These will be explained below:
Often referred to as the bar chart, is chart that depicts mathematical data organised into categories as rectangular bars each having a height and weight in ratio to their values. They can be plotted either way, horizontally and vertically. The vertical bar graph can be called a line graph. Both the axes show the comparison between the classes. Each axis has a category which is represented as different coloured graphs and the other will show values that are measured.
These bar graphs can be grouped or stacked which are used for more complicated data comparisons. As mentioned above, the category of bars is colour coded and represent each class amongst two or more rectangular bars. These are called grouped bar chart. A stacked bar chart has all the different bars depicted different groups on top of each other.
These show us the data in a similar sequence of each rectangular bar, whereas bar graphs which are grouped show the data in order similar to the grouping.
Example: Facebook discovered that toward the finish of 2011, it had over a hundred and forty-six million members in North America. The table below depicts that various age groups , members and their proportions. Using this information, we are to construct a bar graph.
|Age Groups||Member amount||Facebook users in proportion|
We can construct the following bar graph through the above mentioned data:
Previously, we mentioned briefly about how the vertical form of bar graphs are often called line graphs. It is a type of graph which requires relative smaller data sets since they can be plotted in a graph of two axes as a point when each of the axes show data values and its’ frequencies. They are then connected via segments of lines.
Example: In a market research report, conducted with 40 teenagers where they were asked about the number of glasses of water they had. The informed depiction can be seen down below as a table:
|Number of glasses of water they had||Frequency points|
This can be depicted graphically as follows:
These are often called stem and leaf graphs. This is an even better option when the data sets are relatively small. This arises from exploratory data analysis. Similar to Line graph but he instead to dividing into two columns with values and their frequencies we divide the observations in to a leaf and a stem. The leaf entails the final significant digit.
Example: for the statistic’s class on 2017, the grades for the exams are as follows in ascending order: 33; 42; 49; 49; 53; 55; 55; 61; 63; 67; 68; 68; 69; 69; 72; 73; 74; 78; 80; 83; 88; 88; 88; 90; 92; 94; 94; 94; 94; 96; 100.
|4||2 9 9|
|5||3 5 5|
|6||1 3 7 8 8 9 9|
|7||2 3 4 8|
|8||0 3 8 8 8|
|9||0 2 4 4 4 4 6|
This depicts that majority of the grades fell between 60s and 90s.
This is another very popular and highly used way depicting data. It is used for the absolute correct portrayal of numerical distribution. It is similar to the bar graph that we discussed above. Here we need to organise the entire data of values into a series of intervals and then calculate their frequencies. These intervals are usually of equal sizes.
Graphically, this histogram consists of adjacent rectangular bars which can be constructed both vertically as well and horizontally. The x axis which is the horizontal axis shows the variables and the y axis shows the frequency. Here we can also calculate the relative frequency by the following formula:
RF = f / n
For the step by step process of constructing a histogram, we first numerate the bars which depend on the number of intervals. They represent the data and are hence called classes. This can be depicted by the below mentioned example:
Example: Weight of 100 men in ascending order is depicted in the data below :
60; 60.5; 61; 61; 61.5 63.5; 63.5; 63.5 64; 64; 64; 64; 64; 64; 64; 64.5; 64.5; 64.5; 64.5; 64.5; 64.5; 64.5; 64.5 66; 66; 66; 66; 66; 66; 66; 66; 66; 66; 66.5; 66.5; 66.5; 66.5; 66.5; 66.5; 66.5; 66.5; 66.5; 66.5; 66.5; 67; 67; 67; 67; 67; 67; 67; 67; 67; 67; 67; 67; 67.5; 67.5; 67.5; 67.5; 67.5; 67.5; 67.5 68; 68; 69; 69; 69; 69; 69; 69; 69; 69; 69; 69; 69.5; 69.5; 69.5; 69.5; 69.5 70; 70; 70; 70; 70; 70; 70.5; 70.5; 70.5; 71; 71; 71 72; 72; 72; 72.5; 72.5; 73; 73.5 74 The smallest number being 60 so we can decide on our starting point to be below that at 59.95. Similarly our maximum value is 74, so our end value can be 74.05. Next, calculate the width of each bar or class interval. To calculate the width of the bars we use (74.05-59.95) / 8 = 1.76. Here by rounding up we use the width 2 units.
Estimate the intervals we can decipher the following intervals:
59.95 + 2 = 61.95
61.95 + 2 = 63.95
63.95 + 2 = 65.95
65.95 + 2 = 67.95
67.95 + 2 = 69.95
69.95 + 2 = 71.95
71.95 + 2 = 73.95
73.95 + 2 = 75.95
We can include the following histogram:
These are basically line segments depicting points just like line graphs but in a polygonal shape. This is done for the easy interpretation of the observed data. Here we examine the collected information , then decide of the intervals and their frequencies. We then construct the axes and construct the polygon by plotting data points. By over laying the polygons of different samples or data sets we can then compare the distributions.
Example: This examples consists of a frequency distribution table which is then being constructed into a polygon.