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# TOPIC 1: STATISTICAL GRAPHS | GEOGRAPHY FORM 5

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### TATISTICAL GRAPHS

These are the graphs designed to illustrate values of geographical items by means of lines or bars and in turn allow quantitative analysis.

The most useful statistical graphs for the illustration of values include the following.

• Line graphs
• Bar graphs
• Combined bars and line graph

LINE GRAPHS

These are the graphs which use line (s) to illustrate the values of items to give quantitative analysis.

Any line graph has two axes of the following:-

-X – axis; This is also known as the base or horizontal axis. It is used principally to show the value of independent variable like date or places.

-Y – axis: This is also known as the vertical axis. It is used show the values for the dependent variable of like output of crops, minerals etc.

TYPES OF LINE GRAPHS

Linear graphs are extremely varied. They are differently deigned to meet varied functions (roles). With respect to this consideration, linear graphs recognized to be of the following forms:

1. Simple line graph
2. Cumulative line graph
3. Divergent line graph
4. Group line graph
5. Compound line graph

#### Simple line graph

It is a form of line graph, designed to have one line to illustrate the values of one item in relation to dependent and independent variables. i.e. It is designed to show the values of one item per varied date or places.

CONSTRUCTION OF THE SIMPLE LINE GRAPH

Consider the given hypothetical data below showing maize production for country X in 0,000 metric tons (1990 – 1995).

 YEAR PRODUCTION 1990 100 1991 250 1992 300 1993 150 1994 500 1995 400

Procedure

(a) Variables identification

Dependent variable ….. production values

Independent variable ….. Date (Years).

Y – axis …… production values

X – axis ……. Years

(b) Vertical and horizontal scales estimation

Hence; VS is 1 cm to 50000 tons.

Horizontal scale is up on decision

Hence; 1cm represents 1 year

MAIZE PRODUCTION FOR COUNTRY X IN (0,000) Metric tons

Scales:

VS: 1 cm to 50 tons

HS: 1cm to 1 year

Source:

Hypothetical data

Strengths of the simple line graph

It is much easier to prepare as it involves to complicated mathematical works, and also a single line establishes the graph.

From the graph, the absolute values are extracted

It is comparatively easier to read and interpret the values

It has perfect replacement by simple bar graph

Setbacks of the simple line graph

It is a limited graphical method as only suited to represent the value for one item.

Sometimes it becomes difficult to assess the vertical scale if the variation between the highest and lowest values appear wider enough.

Cumulative line graph

It is a form of line graph designed to show the accumulated total values at various dates or possibly places for a single item. This graphical method has no alternative graphical bar method as it can be compared to other linear graphical methods.

Construction of the cumulative line graph

Consider the given hypothetical data below showing maize production for country X.

 YEAR PRODUCTION 1990 50 1991 40 1992 90 1993 100 1994 90 1995 130

Procedure

(a) Variables identification

• Dependent variable ……….. production values
• Independent variable —- Date (Years)

Y – axis ………. Production values

X – axis …………Years

(b)   Vertical and horizontal scales estimation

(c)   Determination of the cumulative values.

 YEAR PRODUCTION CUM VALUES 1990 50 50 1991 40 90 1992 90 180 1993 100 280 1994 90 370 1995 130 500

Hence: VS; 1cm represents 50 tons

Thus; the cumulative lien graph appears as follow.

Cumulative line graph: Maize production for country X.

SCALE:-

VS….. 1cm represents 50 tons

HS ….. 1cm represents 1 year

Source ….. Hypothetical data.

Merits of the cumulative line graph

The graphical method shows cumulative values

From the graph the values can be revealed and quantitatively analyzed

Setbacks of the cumulative line graph

The graphical method is not suited to show cumulative values for more than one item, it is thus; the graphical method  limited for showing the values of a single item.

It needs high skill to reveal the actual values of the item represented

It has no alternative graphical bar method.

Divergent line graph

It is a form of line graph designed to illustrate the increase and decrease of the distribution values in relation to the mean. The graph is designed to have upper and lower sections showing positive and negative values respectively.

The two portions are separated by the steady line graduated with zero value along the vertical line. The steady line also shows the average of all values.

Construction of the divergent line graph

Consider the following tabled data which show export values of coffee for country X in millions of dollars

 YEAR EXPORT VALUES (000,000 dollars) 1952 345 1953 256.5 1954 283 1955 500 1956 335 1957 330.5

(a)  Variables identification

• Dependent variable ……….. Export values
• Independent variable —- Date (Years)

Y – axis ………. Export values

X – axis …………Years

(b)   Computation of the arithmetic mean

·         345 + 256 + 283 + 300 + 335 + 330.5 = 1850

Then;

Computation of the deviation values

1952 345-308 = 37

1953 256.5 – 308 = 52.5

1954 283-308 = -25

1955 300 – 308 = -8

1956 335 – 308 = 27

1957 330.5 – 308 = 22.5

(c)    Estimation of the vertical scale.

Thus: the vertical scale

1cm represents 15 or -15 million dollars

(d)   The graph has to be redrawn accordingly as follows:-

Source:-

Hypothetical data

Scales:-

Vertical scale 1cm represents 15 or 15 tons

Horizontal scale 1cm represents 1 year

Merits of the divergent line graph

The graphical method is useful for showing increase and decrease of the values.

The graphical method shows the average of all values

It has perfect replacement by divergent bar graph

Setbacks of the divergent line graph

The graphical method is not suited to show the increase and decrease values for more than one items, it is thus; the graphical method is limited to a single item.

It needs high skill to reveal the actual values of the item represented.

It is time consuming graphical method as its preparation involves a lot of mathematical works.

It requires high skill to construct the divergent line graph.

Group line graph

It is a form of statistical line graph designed to have more than one lines of varied textures to illustrate the values of more than one items. Group line graph is alternatively known as composite, comparative, and multiple line graph.

Construction of the group line graph

Consider the given data below showing values of export crops from Kenya (Ksh Million).

 Crop/Year 1997 1998 1999 2000 2001 Tea 24,126 32,971 33,065 35150 34,448 Coffee 16,856 12,817 12,029 11,707 7,460 Horticulture 13,752 14,938 17,641 21,216 19,846 Tobacco 1,725 1,607 1,554 2,167 2,887

(a)    Variables identification

Dependent variable …… export values

Independent variable …. Date (years)

Y – -axis………. export values

X – axis………..Years

(b)   Verticals identification

Dependent variable……..export values

Independent variable …… Date (Years)

Hence; VS 1cm represents 5000 export value

Thus; the group line graph appears as follows:-

KENYA: CROPS EXPORT VALUES

Scales:-

Vertical scale: 1cm to 5,000 export values

Source: Kenya Economic Survey 1969

Strengths of the group line graph

It is much easier to prepare as it involves no complicated mathematical works

It is useful graphical method for showing the values of more than one cases.

From the graph, the absolute values are extracted as the values directly shown

It is comparatively easier to read and interpret the values.

It has perfect replacement by group bar graph.

Setbacks of the group line graph

Some times; it becomes difficult to assess the vertical scale if the variation between the highest and lowest values appears wider enough

Crossing of the lines on the graph may confuse the interpreter.

A problem may arise in the selection of the varied line textures.

Compound line graph

It is a line graph designed to have more than one lines compounded to one another by varied shade textures to show the cumulative values of more than one items.

Construction of the compound line graph

Consider the given data below showing cocoa production for the Ghana provinces in 000 tons.

 YEAR/PROV TV Togoland E. province W. province Ashanti 1947/48 40 40 30 35 1948/49 50 60 45 100 1949/50 45 46 89 110 1950/51 45 47 44 124 1951/52 47 23 50 100 1952/53 51 14 57 118

Procedure

(a)    Variables identification

Dependent variable…… export values

Independent variable ….. Date (Years)

Y – -axis……….export values

X – axis………..Years

(b)   Cumulative values determination for the dates.

1947/48 40+40+30+35 = 145

1948/49 50+60+45+100 = 225

1949/50 45+46+89+110 = 290

1950/51 45+47+44+124 = 260

1951/52 47+23+50+100 = 220

1952/53 51+14+57+118= 240

(c)    Vertical and horizontal scales determination

Hence; The vertical scale, 1cm represent 50 tons

Thus the graph appear as follow:-

Strengths of the compound line graph

It is useful graphical method for showing the cumulative values of more than one case.

Depending on the skill the interpreter has, from the graph, the absolute values are extracted as the value directly shown.

It has perfect replacement by compound bar graph

It is comparatively easier to assess the vertical scale to be used.

Setbacks of the compound line graph

It needs high skill to interpret the graph

It needs high skill to construct the graph

A problem may arise in the selection of the varied line textures.

BAR GRAPHS

These are the graphs which use bars to illustrate the values of items to give quantitative analysis.
Any bar graph has two axes

-X-axis; This is also known as the base or horizontal axis. It is used principally to show the values of independent variable like date or places.

– Y – axis; This is also known as the vertical axis. It is used show the values for the dependent variable of like output of crops, minerals etc.

TYPES OF BAR GRAPHS

Like line graphs, bar graphs are also extremely varied as differently designed to meet varied functions. With respect to this consideration, bar graphs categorized into the following:-

1. Simple bar graph
2. Divergent bar graph
3. Group bar graph
4. Compound bar graph
5. Percentage bar graph
6. Population pyramid

Simple bar graph

It is a form of bar graph, designed to have bars of similar texture to illustrate the values of one item in relation to dependent and independent variables. i.e. It is designed to show the values of one item per varied date or places.

Construction of the simple bar graph

Consider the given data below showing cocoa purchase by areas, in 000 metric tons (1953)

 Province Purchase Ashanti 104 W-Province 39 E-Province 45 TV Togo land 22

Procedures

(a)    Variable identification

Dependent variable …… Purchase

Independent variable …. Provinces

Y – -axis………purchase values

X – axis………..Provinces

(b)   Verticals identification

Dependent variable……..export values

Independent variable …… Date (Years)

Thus; the vertical scale: 1cm represents 20,000 tons.

Bar width – 1cm

Bar space = 0.5 cm

The graph has to be constructed accordingly.

COCOA PURCHASE BY PROVINCES (1953/54

Vertical scale; 1cm represents 20000 tons.

Strengths of the simple bar graph

It is much easier to prepare as it involves no complicated mathematical works, and also bars of similar texture established in the graph.

From the graph, the absolute values are extracted.

It is comparatively easier to read and interpret the values

It has perfect replacement by simple line graph.

Setbacks of the simple bar graph

It is a limited graphical method as only suited to represent the values for one  item

Some times; it becomes difficult to assess the vertical scale if the variation between the highest and lowest values appear wider enough.

Divergent bar graph

It is a form of bar graph designed to illustrate the increase and decrease of the distribution values in relation to the mean. The graph is designed to have upper and lower sections showing positive and negative values respectively.

The two portions are separated by the steady lien graduated with zero value along the vertical line. The steady lien also shows the average of all values.

Construction of the divergent line graph

Consider the following tabled data which show export values of coffee for country X in millions of dollars.

 YEAR EXPORT VALUES (000,000 dollars) 1952 345 1953 256.5 1954 283 1955 300 1956 335 1957 330.5

(a) Variable identification

Dependent variable …… Export values

Independent variable …. Date (Years)

Y – -axis………. Export values

X – axis………..Years

(b)   Computation of the arithmetic mean

345 + 256 + 283 + 300 + 335 + 330.5 + 1850

(c)    Computation of the deviation values

1952 345 – 308 = 37

1953 256.5 – 308 = 52.5

1954 283 – 308 = -25

1955 300 – 308 = -8

1956 335 – 308 = 27

1957 330.5 – 308 = 22.5

(d)   Estimation of the vertical scale

Thus: the vertical scale 1cm represents 15 or –15 million dollars

Bar width – 1cm

Bar space – 1cm

(e)    The graph has to be redrawn accordingly as follows.

COFFEE EXPORT VALUES FOR COUNTRY X

In million dollars

Scales:-

Vertical scale 1cm represents 15 or – 15 tons

Horizontal scale: 1cm represents 1 year

Source:- Hypothetical data

Merits of the divergent bar graph

The graphical method is useful for showing increase and decrease of the values

The graphical method shows the average of all values

It has perfect replacement by divergent line graph.

Setbacks of the divergent bar graph

The graphical method is not suited to show the increase and decrease values for more than one item, it is thus; the graphical method is limited to a single item.

It needs high skill to reveal the actual values of the item represented.

It is time consuming graphical method as its preparation involves a lot of mathematical work.

It requires high skill to construct the divergent bar graph.

Grouped bar graph

It is a form of statistical bar graph designed to have more than one bars of varied textures to illustrate the values of more than one items.

Grouped bar graph is alternatively known as composite, comparative, and multiple bar graph.

Construction of the group bar graph

Consider the given data below for cocoa purchase by provinces in Ghana (1947/48 – 1950/51)

 YEAR/PROV TV Togoland E. province W. province Ashanti 1947/48 20 54 28 106 1948/49 26 80 46 126 1949/50 24 67 40 116 1950/51 22 72 45 123

(a)  Variables identification

Dependent variable…… purchase values

Independent variable ….. Date

Y – -axis……… .purchase values

X – axis………..Date

(b)   Vertical scale estimation

Hence; Vs, 1cm to 20,000 tons

Bar width = 1cm

Bar space = 1cm

(c)    The graph should be drawn accordingly.

COCOA PURCHASE BY PROVINCES (1953/54)

Strengths of the grouped bar graph

It is much easier to prepare as it involves no complicated mathematical works

It is useful graphical method for showing the values of more than one cases.

From the graph, the absolute values are extracted as the value are directly shown

It is comparatively easier to read and interpret the values.

It has perfect replacement by group line graph.

Setbacks of the grouped graph

Some times; it becomes difficult to assess the vertical scale if the variation between the highest and lowest values appear wider enough.

A problem may arise in the selection of the varied bar textures.

Compound Bar graph

It is a bar graph designed to have bars divided proportionally showing the cumulative values of more than one items per varied dates or places

Compound bar graph is alternatively known as divided bar graph, or superimposed bar graph.

Construction of the compound bar graph

Consider the given data below showing cocoa production for the Ghana provinces in 000 tons.

Consider the given data below showing cocoa purchase by provinces (1947/48 to 1950/51)

 REGION/YEAR 1947/48 1948/49 1949/50 1950/51 Ashanti 106,000 126,000 116,000 123,000 W.province 28,000 46,000 40,000 45,000 E.Province 54,000 80,000 67,000 72,000 T.Volta 20,000 26,000 24,000 22,000

Procedure

(a)    Variable identification

Dependent variable ….. export values

Independent variable … Date (Years).

Y – -axis………. purchase values

X – axis………..Years

(b)   Cumulative values determination for the dates.

1947/48……….. 106,000 + 28,000 + 54,000 + 20,000 = 208

1948/49………… 126,000 + 46,000 + 80,000 + 26,000 = 278,000

1949/50 ………… 116,000 + 40,000 + 67,000 + 24,000 = 247,000

1950/51…………..123,000 + 45,000 + 72,000 + 22,000 = 262,000

(c)    Vertical scale determination.

Thus; the VS … 1cm represents 50,000 tons.

The graph should be drawn accordingly.

COCOA PURCHASE BY PROVINCE (1947/48 – 1950/51)

Strength of the compound bar graph

It is useful graphical method for showing the cumulative values of more than one cases

Depending on the skill the interpreter has, from the graph, the absolute values are extracted as the value directly shown.

It has perfect replacement by compound line graph

It is comparatively easier to assess the vertical scale to be used.

Setbacks of the compound bar graph

It  needs high skill to interpret the graph

It needs high skill to construct the graph

A problem may arise in the selection of the varied textures of the proportional segments

It is very fedious /tiresome as it involve mathematical calculation
It is time consuming in preparation

Percentage bar graph

In percentage bar graph, all bars must be drawn on the same height representing 100% and suitable scale is chosen such as 5, 10, 20 etc, and marked along the sides. The percentages of the total each area stands for must start from zero line. Also it is advised to include the actual percentages of the face of the bars.

Construction of the Percentage bar graph

Consider the given data below showing cocoa purchase by provinces (1947/48 to 1950/51)

 REGION/YEAR 1947/48 1948/49 1949/50 1950/51 Ashanti 106,000 126,000 116,000 123,000 W.province 28,000 46,000 40,000 45,000 E.Province 54,000 80,000 67,000 72,000 T.Volta 20,000 26,000 24,000 22,000

Procedure

(a)    Variables identification
Dependent variable ….. export values
Independent variable … Date (Years).
Y-axis………. purchase values
X-axis………..Years

(b)   Cumulative values determination for the dates.

1947/48……….. 106,000 + 28,000 + 54,000 + 20,000 = 208

1948/49………… 126,000 + 46,000 + 80,000 + 26,000 = 278,000

1949/50 ………… 116,000 + 40,000 + 67,000 + 24,000 = 247,000

1950/51…………..123,000 + 45,000 + 72,000 + 22,000 = 262,000

(c)    The percentages by provinces in each year determination.
1947/48:

1948/49:

1949/50:

1950/51:

Hence; VS; 1 cm represents 20%
The percentage bar graph should be drawn accordingly as follow:-

COCOA PURCHASE BY PROVINCES (1947/48 – 1950/51)

Vertical scale; 1cm represents 20%

Strengths of the percentage bar graph

It is useful graphical method for showing the values of more than one cases

The data represented appear in a more simplified form as given in percentages.

It is comparatively easier to assess the vertical scale to be used

Setbacks of the percentage bar graph

It does not give the absolute values

It needs high skill to interpret the graph

It needs high skill to construct the graph

A problem may arise in the selection of the varied textures of the proportional segments

It consumes much time to be prepared.

#### Population pyramid graph

It is a form of bar graph designed to show population distribution by age and sex. It is a double bar chart showing the age sex structure of the population. It  consists of two sets of horizontal bars; one is for each sex showing either the p percentages or absolute numbers.

Rules for drawing the population pyramid graph

It is a principle in drawing population pyramid; the number of male population illustrated by the left set of bars; while that of females by the right set of bars.

The young population distribution is always at the bottom while that of old at the top.

Usually the last age group should be left open handled because; some people may survive beyond 100 years and their number have been omitted.

The bottom scale can be graduated as percentages or absolute numbers.

If percentages are opted to be used; the total population of both combined sexes should be used to compute the percentages.

After all the bars have been drawn, they can be shaded in one colour or separated colours for each sex.

CONSTRUCTION OF THE POPULATION PYRAMID

There are two techniques of drawing the horizontal bars of an age sex pyramid. In the first

technique, the bars are drawn proportionally to the actual population numbers (absolute values).

In the second technique, the bars are drawn to represent percentages.

 Age group Male Female Total 0 – 4 2291936 2242966 4534902 5-9 2000580 1962556 3963136 10-14 2034980 2003655 4038635 15-19 1681984 1721194 3403178 20-24 1328529 1504389 2832918 25-29 1094909 11664594 2259503 30-34 840692 845230 1685922 35-39 695263 723749 1419012 40-44 516502 516989 1033491 45-49 419841 418987 838828 50-54 344639 340167 684806 55-59 223691 236325 460016 60-64 194513 214715 409228 65-69 140969 160364 301333 70-74 118601 135524 254125 75-79 79166 81620 160786 80+ 95300 121038 216338 Age not stated 103487 86956 190443 All ages 14205589 14481018 28686607

The absolute value technique

The following steps are followed when constructing a population pyramid using absolute values.

Decide a suitable scale for the horizontal axis (baseline) by considering the values of the biggest and smallest age group, as well as the size of the paper on which the pyramid is to be drawn. Horizontal scale is determined as follows.

Hence by considering the data in the table, scale of 1cm to represent 400,000 people would be suitable.

Choose a suitable scale for the vertical axis. This scale will determine how wide the bars will be and also the interval between the age groups. The width of the bars should not exceed 6mm otherwise the pyramid will look untidy.

Take a clean graph paper and on it draw horizontal axis at least 3 cm from the bottom of the page. Draw two vertical axes of 1 cm apart and about 10 cm long, until they touch the horizontal axis.

Where the vertical axes touch the horizontal axis, mark as zero. On the horizontal axis, and at intervals of 1cm from the zero mark on the both sides, mark of the values representing the female and male population

In the middle column, fill in the age groups starting with the youngest at the bottom. The age groups should be within the width of the horizontal bars.

Using the horizontal scale, and starting with the first age group for females, draw a bar from the vertical axis on the right hand side of the central column towards the right to represent the female population of that group. The scale chosen in step 1 above will determine the length of the bar.

From the left hand side of the vertical axis, draw a bar representing the male population of the same age group. Steps 6 and 7 should be repeated for all the subsequent age group until the last one has been represented.

Fig. 1.1 Kenya: Population by age and sex, 1999

The percentages technique

By this technique, the values for population distribution by age and sex given in percentages. The percentages of each female or male group over the total populations is calculated from the absolute values in our example and a new set of data will be derived from data in the table.

This new data will be used to draw the graph. An example on how to calculate the percentage values is shown below.
The application for calculating the percentage is as follows.

For instance:

The absolute values for the females aged between 0-4 years from the table is 2242 966, while that for males is 2291936. The total populations according to the 1999 census, was 28686607. Therefore  the percentage of females is as follows:-

The percentage of male is as follows:-

The worked out percentage values from the figure in the table are given in the table next page.

 Age Group 5male %female Total 1-4 8.0 7.8 15.8 5-9 7.0 6.8 13.8 10-14 7.1 7.0 14.1 15-19 5.9 6.0 11.9 20-24 4.6 5.2 9.8 25-29 3.8 4.1 7.9 30-34 2.9 2.9 5.8 35-39 2.4 2.5 4.9 40-44 1.8 1.8 3.6 45-49 1.5 1.5 3.0 50-54 1.2 1.2 2.4 55-59 0.8 0.8 1.6 60-64 0.7 0.7 1.4 65-69 0.5 0.6 1.1 70-74 0.4 0.5 0.9 75-79 0.3 0.3 0.6 80+ 0.3 0.4 0.7

After the calculation of the percentages, the following steps should be taken to come up with the age – sex pyramid.

Choose a suitable scale for the horizontal axis by considering the highest and the lowest percentages in the table. According to the values I the table, a scale of 1cm is representing 1% would be suitable.

Follow step 2 and 3 as outlined under the absolute values techniques discussed earlier.

Where the vertical axis touch the horizontal axis, mark zero and at intervals of 1cm, mark of the percentage value towards the right for females, and towards left for the males.

The age group should be indicated in the middle column just as we did when constructing an age sex pyramid using absolute values..

Using the horizontal scale and starting with age group 0-4 draw a bar on the right hand side to represent the percentage values of the female population in this age group. In our example, the percentage is 7.8 Draw a similar bar on the left hand side to represent the value of the male population, which in our case is 0.8.

Draw bars to represent all the age groups follow steps 9 and 10 under the absolute value technique to complete the pyramid.

Kenya population by age:

Note

Pyramid may also be for the purpose of making comparison either in terms of time or location. This can be by means of a double combined population pyramid. The double combined population pyramid looks as follows.

It is visually attractive method of presenting data.

A variety of information is shown on the same graph. The details include; age, sex and number of people

It can be used to compare the age sex structure of number of countries

It gives a clear picture and summary of the population composition of a country.

It is tedious to construct because it involves many values.

It is difficult to tell the exact values represented because of the small scale of the horizontal axis.

Reasons for the differences in population numbers cannot be obtained from the graph directly. Therefore additional information has to be thought from elsewhere.

COMBINED BAR AND LINE GRAPH

It is a form statistical graph designed to have both bars and line to show two attributes whose values appear in varied unit. It is basically employed to show the values of rainfall and temperature together in a year.

In the graph, the bars used to illustrate the values on amount of rainfall in mm or inch, while the line is used to illustrate the values on amount of temperature in 0C or 0F. This is also known as climo graph.

Construction of the bar and line graph

Consider the following climatic data for Dar-win weather station Australia.

 Month J F M A M J J A S O N D Temp oC 28.9 27.8 28.9 29 26.7 26 25.1 26.4 28.1 29.7 29.8 29 Rain(mm) 388 330 246 114 17.8 5 2.5 2.5 12.7 53.3 132 261

Procedure

(i) Identification of the variables

· Dependent variable – Rain and temperature values

· Independent variable – Data (months).

Y – -axis – Rain and temperature values

X – axis………..months

(ii) Estimation of the vertical scale to be used

Thus; the vertical scale for rainfall is 1cm to 50mm.

Thus; the vertical scale for temperature is 1 cm to 10 c

(iii) The graph has to be drawn as follows;

CLIMATIC CONDITION FOR DARWIN AUSTRALIA

Strengths of the combined bar and line graph

It is useful graphical method for showing the distribution values of climate

It is more illustrative, as it provides visual idea to the users in statistics.

It allows the easy making of quantitative analysis

Setbacks of the combined bar and line graph

It is more illustrative, as it provides visual idea to the users in statistics

Needs high skill to make quantitative analysis from the graph

It is time consuming graphical method in construction

It needs high skill to construct the graph

It is tedious as it involves mathematical calculation

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