## 5 ADVANTAGES OF A LINE GRAPH IN REPRESENTING STATISTICAL DATA

A line graph is a type of chart that uses lines to connect points to show how data changes over time. The points are usually plotted on a coordinate plane, with the x-axis representing the time or independent variable and the y-axis representing the data or dependent variable.

Line graphs are a versatile tool that can be used to visualize a wide variety of data. They are often used to track changes in population, economic indicators, weather patterns, and other phenomena.

## The following are advantages of line graph to represent statistical data

### Easy to draw

Line graphs are relatively easy to draw, even for people who are not familiar with graphing techniques. This makes them a good choice for people who want to create their own graphs to represent statistical data.

### Allow comparison

Line graphs can be used to compare two or more sets of data by plotting the data points for each set on the same graph. This makes it easy to see how the data sets are related to each other and to identify any trends or patterns.

### Easy to read and interpret

Line graphs are also easy to read and interpret. The data points are plotted on a grid, which makes it easy to see the values of the data and to identify any changes in the data over time. The lines connecting the data points can also be used to visualize trends or patterns in the data.

### Clear visual impression

Line graphs can create a clear visual impression of the data. This makes them a good choice for presentations or reports where you want to communicate the data in a way that is easy to understand.

### Can be used to show wide range of data

Line graphs can be used to show a wide range of data, from small changes to large changes. This makes them a versatile tool that can be used to represent a variety of statistical data.

### To show trends over time

Line graphs are a great way to show how data changes over time. This can be useful for tracking things like population growth, economic growth, or the spread of a disease.

For example, a line graph could be used to show the number of people living in Tanzania over time. The graph would start with the number of people in 1961 and then show how the number has changed each year since then. This would allow you to see the overall trend in population growth, as well as any spikes or dips.

### To show the relationship between two or more variables

Line graphs can also be used to show the relationship between two or more variables. This can be useful for understanding how different factors affect each other.

For example, a line graph could be used to show the relationship between the price of gasoline and the number of miles driven. The graph would show how the price of gasoline has changed over time, and how the number of miles driven has changed over time. This would allow you to see how the two variables are related to each other.

### To show comparisons between different groups of data

Line graphs can also be used to show comparisons between different groups of data. This can be useful for understanding how different groups are performing or how they are different from each other.

For example, a line graph could be used to show the average income of different countries over time. The graph would show how the average income has changed in each country, and how the countries compare to each other. This would allow you to see which countries are doing well economically and which countries are struggling.

### To show the distribution of data

Line graphs can also be used to show the distribution of data. This can be useful for understanding how data is spread out and where the most common values are.

For example, a line graph could be used to show the distribution of heights in a population. The graph would show how many people are of each height, and how the heights are distributed. This would allow you to see what the average height is and how many people are taller or shorter than average.

### To show the impact of changes in one variable on another variable

Line graphs can also be used to show the impact of changes in one variable on another variable. This can be useful for understanding how one factor affects another.

For example, a line graph could be used to show the impact of a new policy on the number of people who are unemployed. The graph would show how the number of unemployed people has changed since the policy was implemented. This would allow you to see whether the policy has had the desired effect.

These are just a few of the advantages of using a line graph in representing statistical data. Line graphs are a versatile tool that can be used to visualize data in a variety of ways. When used correctly, they can be a powerful tool for understanding and communicating data.

## Here are some additional things to keep in mind when using line graphs:

• Choose the right scale: The scale of the line graph should be appropriate for the data that you are plotting. If the scale is too small, the changes in the data will be difficult to see. If the scale is too large, the graph will be cluttered and difficult to read.
• Use clear labels: The labels on the axes of the line graph should be clear and concise. They should also be consistent with the units of measurement that are being used.
• Use a legend: If you are plotting multiple lines on the same graph, you should use a legend to identify each line. This will help the reader to understand what each line represents.
• Use a title: The title of the line graph should be clear and concise. It should also accurately describe the data that is being plotted.

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A pie chart or circle chart is a circular statistical chart graph, which is divided into slices to illustrate numerical proportions.

While it is named for its resemblances to a pie which have been sliced, there is a variation in the way it can be presented.

• display relative proportions of multiple classes of data.

• summarize a large data set into visual form.
• pie charts are easily understood due to its widespread use in business and media
• pie charts permit a visual check of the reasonableness or accuracy of the calculation.
• pie charts are visually simpler than other types of graphs.
• size of the circle can be made proportional to the quantity it represents.

• it does not easily reveal exact values. Values are expressed in terms of percentages or ratio therefore it is not easy to know the exact value represented

• the pie chart does not easily show changes over time
• pie charts fail to reveal key assumptions, causes, effects, or patterns
• pie charts can easily be manipulated to yield false impressions

## HOW TO CALCULATE STANDARD DEVIATION FOR GROUPED AND UNGROUPED DATA

Non-Grouped Data
Non-grouped data is just a list of values. The standard deviation is given by the formula:

s means ‘standard deviation’.
S means ‘the sum of’.
means ‘the mean’

Example
Find the standard deviation of 4, 9, 11, 12, 17, 5, 8, 12, 14
First work out the mean: 10.222

Now, subtract the mean individually from each of the numbers given and square the result.

This is equivalent to the (x – )² step. x refers to the values given in the question.

Now add up these results (this is the ‘sigma’ in the formula): 139.55
Divide by n. n is the number of values, so in this case, is 9. This gives us: 15.51
And finally, square root this: 3.94

The standard deviation can usually be calculated much more easily with a calculator and this may be acceptable in some exams. On my calculator, you go into the standard deviation mode (mode ‘.’).

Then type in the first value, press ‘data’, type in the second value, press ‘data’.

Do this until you have typed in all the values, then press the standard deviation button (it will probably have a lower case sigma on it). Check your calculator’s manual to see how to calculate it on yours.

NB: If you have a set of numbers (e.g. 1, 5, 2, 7, 3, 5 and 3), if each number is increased by the same amount (e.g. to 3, 7, 4, 9, 5, 7 and 5), the standard deviation will be the same and the mean will have increased by the amount each of the numbers was increased by (2 in this case).

This is because the standard deviation measures the spread of the data. Increasing each of the numbers by 2 does not make the numbers any more spread out, it just shifts them all along.

Grouped Data
When dealing with grouped data, such as the following:

the formula for standard deviation becomes:

Try working out the standard deviation of the above data. You should get an answer of 1.32 .
You may be given the data in the form of groups, such as:

In such a circumstance, x is the midpoint of groups.

## arithmetic mean

arithmetic mean is the average of all values in a set of distribution.

it is determined by adding up all values and dividing by the sum of observations added.

arithmetic mean is used to assess the distribution value whether was high or low

### advantages of the arithmetic mean

• it is easy to calculate and the majority of people understand it
• it is used to check the values if high or low
• it can be used for further calculation; for example arithmetic mean is used to calculate standard deviation

• arithemetic mean has the big weakness of being pulled toward an outlier (extreme score)
• it need high mathematical knowledge to calculate arithematic mean for grouped data

## 9 ADVANTAGES OF BAR GRAPH

A bar graph is a pictorial rendition of statistical data in which the independent variable can attain only certain discrete values. The dependent variable may be discrete or continuous. The most common form of bar graph is the vertical bar graph, also called a column graph.

In a vertical bar graph, values of the independent variable are plotted along a horizontal axis from left to right. Function values are shown as shaded or colored vertical bars of equal thickness extending upward from the horizontal axis to various heights.

In a horizontal bar graph, the independent variable is plotted along a vertical axis from the bottom up. Values of the function are shown as shaded or colored horizontal bars of equal thickness extending toward the right, with their left ends vertically aligned.

## types of bar graphs

bar graphs are mainly classified into two types

apart from the vertical and horizontal bar graphs, there are two more types of bar graph namely; grouped bar graph and stacked pr compound bar graph

## The following are advantages of a bar graph:

• Show each data category in a frequency distribution

• Display relative numbers or proportions of multiple categories
• Summarize a large amount of data in a visual, easily interpretable form
• Make trends easier to highlight than tables do
• it helps in studying patterns over long period of time
• it is used to compare data sets. data sets are independent of each other
• most widely used method of data representation. therefore, it is used by various industries
• Estimates can be made quickly and accurately
• Permit visual guidance on accuracy and reasonableness of calculations
• Accessible to a wide audience
• can easily compare two or three data sets

## what is dot map?

Dot maps or dot distribution map (also known as dot density map) is a map type that uses a dot symbol to show the presence of a feature or phenomenon.

Dot maps rely on a visual scatter to show spatial patterns.

in other words, A dot map is a statistical map that uses dots of fixed size to represent a fixed number of units in a particular area.

They employ a base map of a concerned area and a dot is drawn exactly on the appropriate location on the map.

they are useful in representing statistical data like population, plants in the forest, and so on

population density maps are often dotted maps

all dot maps must be drawn on an equal-area map projection. this is critical because using map projection which does not preserve the size of the area will distort the perceived density of the dots

## types of dot maps

one to one dot maps where one dot represents one object or count

one to many dot maps in which one dot stands for number of things or a value (for example 1 dot represent 10000 acres of wheat production

## The following are advantages of dot maps:

• If well constructed it shows the distribution and comparative densities
• It is easier to show variation in the distribution of a wide variety of commodities if it is presented using different colors.
• Dot maps are used to represent a wide range of items like population, the value of minerals, crops, and so forth
• dot maps are easy to read even to layman
• by counting the symbols it is possible to determine the original data

• They are very easy to construct compared to proportional circles
• It is very easy to compare the distribution of items considering the concentration of dots.
• the dots can be converted into choropleth or isopleth but these maps can not be transfered into dot maps
• more than one element can be shown on single map by using multiple dot map method
• this is the best method for showing the absolute figures
• dot maps work fine in black and white, when colour is not an option
• your data need not be tied to enumeration units and hence some of the concern inherent in the choropleth maps can be side stepped with dot maps.

## uses of dot maps

dot maps are used to visualize distribution and densities of a big number of discrete distributed single objects by using dots which represent a constant number of objects

## quantitative symbols of fixed size

the most simple dot maps uses a point symbol for a defined number of identical objects. the difficulty is to find an appropriate shape and size for the symbol as well as the value of it.

## quantitative symbol of variable size

quantitative symbol of variable size can be used if the map depict an area where the object density is heterogenous and where it is difficult to find an appropriate symbol of fixed size. therefore different sizes of the symbol can be assigned to different values

## example of data set appropriate for dot maps

• the distribution of car dealership in belgium (1 dot=1 dealership)
• earthquake epicentre across pacific for the last 10 years I1 dot = 1 epicentre)
• number of people by country (1 dot = 100000 people)

## things to keep in mind when making dot maps

• include the legend that shows how many units of data are represented with each dot
• use the same size dots and ensure the size of each dot is appropriate for the scale and the size of the map
• ensure that colours are distinguishable
• use an albers equal area projection when making dot maps

## 2 CLASSIFICATION OF STATISTICS

Statistics being the scientific and systematic methods dealing with numerical facts is broadly categorized into two types depending on how data is handled.

The two main categories of statistics are descriptive and inferential statistics.

## Descriptive statistics

this deals with recording, summarizing, analyzing and presentation of numerical facts that have been actually collected.

Descriptive statistics is the term given to the analysis of data that helps describe, show or summarize data in a meaningful way such that, for example, patterns might emerge from the data.

Descriptive statistics do not, however, allow us to make conclusions beyond the data we have analyzed or reach conclusions regarding any hypotheses we might have made.

They are simply a way to describe our data. Descriptive statistics are very important because if we simply presented our raw data it would be hard to visualize what the data was showing, especially if there was a lot of it.

Descriptive statistics, therefore, enables us to present the data in a more meaningful way, which allows a simpler interpretation of the data.

For example, if we had the results of 100 pieces of students’ coursework, we may be interested in the overall performance of those students.

We would also be interested in the distribution or spread of the marks. Descriptive statistics allow us to do this.

Typically, there are two general types of statistics that are used to describe data they are a measure of central tendency and measure of spread

Inferential statistics

this makes inferences about populations using data drawn from the population.

Instead of using the entire population to gather the data, the statistician will collect a sample or samples from the millions of residents and make inferences about the entire population using the sample.

With inferential statistics, you are trying to reach conclusions that extend beyond the immediate data alone.

For instance, we use inferential statistics to try to infer from the sample data what the population might think.

Or, we use inferential statistics to make judgments of the probability that an observed difference between groups is a dependable one or one that might have happened by chance in this study.

Thus, we use inferential statistics to make inferences from our data to more general conditions; we use descriptive statistics simply to describe what’s going on in our data.