Unit 6: Quantitative Techniques in Economics | Class 10 Economics Notes

Importantedunotes.com

Unit 6: Quantitative Techniques in Economics

Class 10 Economics

Unit 6 Chapter 1 Presentation of Data

For SEE Board Exam Preparation: Theoretical Notes, Complete Q&A, and All Diagrams

Welcome to the complete study guide on Unit 6 Chapter 1 Presentation of Data of Class 10 Economics for Nepal SEE board exam preparation.

This page covers all types of diagrams: Simple Bar, Multiple Bar, Sub-divided Bar, Percentage Bar, Pie Charts, Line Graphs, and Histograms.

Explore: Class 10 Economics Notes

1. Theoretical Notes

Presentation of Data

The process of presenting data in the form of tables, diagrams, graphs, and descriptive text is called Presentation of Data. This process helps to clearly understand the data, identify patterns within it, make comparisons and analyses, and make informed decisions.

In this chapter, among the various methods of data presentation, only diagrammatic and graphical (graphic) representation are studied.

1.1 Diagrammatic Representation

The process of presenting data in the form of line diagrams, bar diagrams, pie charts, pictograms, and cartograms is called Diagrammatic Representation.

Points to consider when making a diagrammatic representation:

(a) An appropriate title and heading must be given to each diagram.

(b) What is shown on the vertical and horizontal axes of the diagram must be clearly stated.

(d) Different colours or symbols should be used to make the diagram attractive.

(A) Simple Bar Diagram

A diagram in which data having only a single characteristic or variable is presented through bars (columns) of equal width and heights/lengths corresponding to the value of the data is called a Simple Bar Diagram.

(B) Multiple Bar Diagram

A diagram used to present data that has two or more related characteristics or variables in a comparative manner is called a Multiple Bar Diagram.

(C) Sub-divided Bar Diagram

A diagram in which a single bar is divided into various sub-parts to present the total value and its various components is called a Sub-divided Bar Diagram (also known as a Stacked Bar Diagram). In this, the total height of the bar represents the total value.

(D) Percentage Sub-divided Bar Diagram

A diagram in which different components are converted into their percentage of the total value and then divided and presented within a single bar is called a Percentage Sub-divided Bar Diagram. In this, the total height of all bars is always equal to 100 percent.

(E) Pie Chart

A diagram in which the total value of any data is considered a complete circle (360 degrees) and its various components are presented as different sectors of that circle is called a Pie Chart.

Formula: Angle = (Value of the relevant component / Total value) × 360°

1.2 Graphical (Graphic) Representation

A diagram made on graph paper by plotting points on the X-axis and Y-axis and then connecting those points is called Graphical Representation.

(A) Simple Line Graph

A diagram made on graph paper by plotting points for a single variable and time, and then connecting those points with straight lines, is called a Simple Line Graph. Generally, time is placed on the X-axis and the value of the variable on the Y-axis.

(B) Multiple Line Graph

A diagram in which two or more variables are presented on the same graph paper using different lines is called a Multiple Line Graph.

(C) Histogram (Frequency Distribution Diagram)

A method of presenting data given in a continuous series with frequency (frequency distribution) using rectangles is called a Histogram. In a histogram, the rectangles are joined together because the class intervals are continuous — the upper boundary of one class immediately meets the lower boundary of the next, leaving no gaps between them.

1. Give very short answers to the following questions:

(a) What are the methods of presenting data?

Answer: The four main methods used to present collected data in a simple and easily understandable way are:
1. Textual (Descriptive) Presentation
2. Tabular Presentation
3. Diagrammatic Presentation
4. Graphical Presentation

(b) What is a Simple Bar Diagram?

Answer: A diagram made using separate rectangular bars of equal width but different heights — according to the values of the data — to show statistical data that has only one attribute or characteristic in a comparative manner is called a Simple Bar Diagram.

Answer: In a Sub-divided Bar Diagram, the total height of each bar differs according to its total value, whereas in a Percentage Bar Diagram, the total height of all bars is always the same (100 percent), and each segment represents only the percentage of the corresponding component.

(d) What kind of data is most suitable for presentation in a Multiple Bar Diagram?

Answer: Data that has two or more interrelated variables or characteristics — such as the import and export figures of different years, or the production of various crops — is most suitable for a comparative presentation in a Multiple Bar Diagram.

(e) What kind of data is presented in a Time Series Line Graph?

Answer: Historical or sequential data that changes continuously over time intervals (such as years, months, weeks, or days) — for example, annual gross domestic product, per capita income, or population growth rate — is presented in a Time Series Line Graph.

(f) Which variables are measured on the horizontal and vertical axes of a Time Series Line Graph?

Answer: Time (the independent variable, such as year or month) is measured on the horizontal axis (X-axis), and the value or quantity of the data (the dependent variable, such as production or income) is measured on the vertical axis (Y-axis).

(g) Why are the rectangular bars in a Histogram joined together?

Answer: The data presented in a Histogram is based on class intervals of a Continuous Series, in which the upper boundary of one class is immediately connected to the lower boundary of the next class. Since there is no gap between them, the rectangular bars are joined together.

2. Solve the following statistical questions:

(a) The total income of a household has been divided into consumption expenditure and savings and shown in the table below. Based on this table, prepare a Simple Bar Diagram: Simple Bar

Particulars	Amount (Rs.)
Consumption	20,000
Saving	5,000

Scale: Y-axis → 1 unit = Rs. 5,000 Consumption = 20,000 → 4 units | Saving = 5,000 → 1 unit

Figure (a): Household Consumption and Saving — Simple Bar Diagram

(b) The population of Nepal by geographical region is shown in the table below. Present this table as a Simple Bar Diagram: Simple Bar

Geographical Region	Population (in Lakhs)
Himalayan	17.73
Hill	117.57
Terai	156.34

Scale: Y-axis → 1 unit = 20 Lakhs | Source: National Census, 2078

Figure (b): Population of Nepal by Geographical Region — Simple Bar Diagram

(c) The table below shows the various expenditure heads of a household over a period of one month. Present these expenditure heads and amounts in a Simple Bar Diagram: Simple Bar

Expenditure Head	Amount (Rs.)
Education	12,000
Health	5,000
Communication	3,000
Food	17,000
Clothing	7,000
Others	6,000

Scale: Y-axis → 1 unit = Rs. 2,000

Figure (c): Monthly Household Expenditure — Simple Bar Diagram

(d) The table below shows electricity consumption by sector over a specific period. Based on this, prepare a Sub-divided Bar Diagram: Sub-divided Bar

Sector	Electricity Consumption (kW)	Cumulative
Household	1,200	1,200
Industry	1,500	2,700
Trade and Commerce	300	3,000
Others	100	3,100
Total	3,100

Scale: Y-axis → 1 unit = 500 kW | Total: 3,100 → 6.2 units

Figure (d): Electricity Consumption by Sector — Sub-divided Bar Diagram

(e) Based on the table below, prepare a Sub-divided Bar Diagram: Sub-divided Bar

District	Paddy	Maize	Wheat	Total
Jhapa	1,200	800	300	2,300
Morang	1,500	500	450	2,450
Sunsari	900	700	400	2,000

Scale: Y-axis → 1 unit = 500 metric tons

Figure (e): District-wise Food Crop Production — Sub-divided Bar Diagram

(f) Present the table below as a Percentage Bar Diagram: % Bar

Expenditure Head	Amount (Rs.)	Percentage (%)	Cumulative (%)
Education	12,000	24%	24
Health	5,000	10%	34
Communication	3,000	6%	40
Food	17,000	34%	74
Clothing	7,000	14%	88
Others	6,000	12%	100
Total	50,000	100%

Figure (f): Family Expenditure — Percentage Bar Diagram

(g) The table below shows the percentage contribution of agriculture, industry, and the service sector to the GDP of three countries. Based on this, prepare a Percentage Bar Diagram: % Bar

Country	Agriculture (%)	Industry (%)	Service (%)	Total
A	25	30	45	100
B	20	35	45	100
C	35	25	40	100

Cumulative % — A: 25, 55, 100 | B: 20, 55, 100 | C: 35, 60, 100

Figure (g): Sectoral Contribution to GDP of Three Countries — Percentage Bar Diagram

(h) Based on the table below, prepare a Multiple Bar Diagram: Multiple Bar

Fiscal Year	Import (Rs. Crore)	Export (Rs. Crore)
2077/78	1,500	400
2078/79	1,920	350
2079/80	1,612	375
2080/81	1,700	410

Scale: Y-axis → 1 unit = 200 crore

Figure (h): Import and Export — Multiple Bar Diagram

(i) Based on the table below, prepare a Multiple Bar Diagram: Multiple Bar

Fiscal Year	Tax Revenue (Rs. Crore)	Non-Tax Revenue (Rs. Crore)
2077/78	800	200
2078/79	850	220
2079/80	900	250

Scale: Y-axis → 1 unit = 100 crore

Figure (i): Tax and Non-Tax Revenue — Multiple Bar Diagram

(j) Based on the table below, prepare a Multiple Bar Diagram: Multiple Bar

Fiscal Year	Education (Billion)	Health (Billion)	Roads (Billion)
2077/78	200	120	150
2078/79	220	130	170
2079/80	245	180	200

Scale: Y-axis → 1 unit = 50 billion

Figure (j): Government Expenditure — Multiple Bar Diagram

(k) Based on the table below, construct a Pie Chart: Pie Chart

Cost Head	Cost (Rs.)	Angle
Labour	1,200	90°
Cement	1,600	120°
Wood	600	45°
Iron	800	60°
Sand	400	30°
Miscellaneous	200	15°
Total	4,800	360°

Formula: Angle = (Cost / 4,800) × 360°

Figure (k): Construction Cost — Pie Chart

(l) The share of various goods in total exports is presented in the table below. Based on this, construct a Pie Chart: Pie Chart

Goods	Percentage (%)	Angle
Agricultural Products	35%	126°
Handicrafts	25%	90°
Clothing	22%	79.2°
Others	18%	64.8°
Total	100%	360°

Figure (l): Share of Goods in Total Exports — Pie Chart

(m) The table below shows commercial bank branches by province. Present this as a Pie Chart: Pie Chart

Province	Number of Branches	Angle
Koshi	762	54.0°
Madhesh	581	41.2°
Bagmati	1,842	130.5°
Gandaki	605	42.9°
Lumbini	745	52.8°
Karnali	216	15.3°
Sudurpashchim	330	23.4°
Total	5,081	360°

Formula: Angle = (Branches / 5,081) × 360° | Source: Economic Survey, 2081/82

Figure (m): Commercial Bank Branches by Province — Pie Chart

(n) The table below shows the GDP growth rate of different years. Based on this, construct a Time Series Line Graph: Line Graph

Year (A.D.)	2014	2015	2016	2017	2018	2019	2020	2021	2022
GDP Growth Rate (%)	4.2	3.8	5.0	5.5	6.1	-1.8	2.5	4.7	5.2

Note: In 2019, the growth rate became negative (-1.8%) due to COVID-19.

Figure (n): GDP Growth Rate — Time Series Line Graph

(o) Present the data given below in an appropriate Line Graph: Multiple Line

Year (B.S.)	2075	2076	2077	2078	2079	2080
Income (Rs.)	40,000	55,000	80,000	75,000	60,000	1,00,000
Expenditure (Rs.)	35,000	42,000	60,000	61,000	55,000	80,000

Scale: Y-axis → 1 unit = Rs. 10,000

Figure (o): Income and Expenditure — Multiple Line Graph

(p) The frequency table below shows the marks obtained in Economics by Class 10 students. Present this as a Histogram: Histogram

Marks (Class Interval)	Number of Students
10–20	6
20–30	13
30–40	10
40–50	20
50–60	25
60–70	18

Scale: Y-axis → 1 unit = 5 students | Bars are joined together

Figure (p): Students’ Marks — Histogram

(q) Based on the data below, construct a Histogram: Histogram

Wages (Rs. in hundreds)	Number of Workers
5–15	5
15–25	3
25–35	8
35–45	9
45–55	12

Scale: Y-axis → 1 unit = 2 workers

Figure (q): Wages and Number of Workers — Histogram

4. Exercise 3 — Solve the following questions:

(a) Present the table below as a Percentage Bar Diagram: % Bar

Income Head	Family ‘A’ (Rs.)	‘A’ %	Cumul. ‘A’	Family ‘B’ (Rs.)	‘B’ %	Cumul. ‘B’
Wages	32,000	50.00%	50.00	22,000	41.51%	41.51
Interest	2,000	3.13%	53.13	4,000	7.55%	49.06
Profit	15,000	23.44%	76.57	7,000	13.21%	62.27
House Rent	12,000	18.75%	95.32	15,000	28.30%	90.57
Other / Misc.	3,000	4.69%	100.00	5,000	9.43%	100.00
Total	64,000	100%		53,000	100%

Figure (a): Income Sources of Two Families — Percentage Bar Diagram

(b) The table below shows data on fruit sales in different years. Present this data as a Multiple Bar Diagram: Multiple Bar

Year	Apple	Orange	Mango	Banana
2077	220	500	125	700
2078	230	410	180	550
2079	190	450	220	600
2080	250	400	200	640

Scale: Y-axis → 1 unit = 100 kg

Figure (b): Fruit Sales — Multiple Bar Diagram

Energy Source	2081 (W)	Angle 2081	2082 (W)	Angle 2082
Hydropower	900	215.0°	945	281.9°
Thermal	250	59.7°	190	56.7°
Solar	250	59.7°	50	14.9°
Coal	100	23.9°	12	3.6°
Others	7	1.7°	10	3.0°
Total	1,507	360°	1,207	360°

Figure (c): Energy Consumption Year 2081 and 2082 — Two Pie Charts

(d) The table below shows the monthly expenditure of two families under different heads. Based on this table, construct Pie Charts: Pie Chart

Expenditure Head	‘A’ (Rs.)	Angle ‘A’	‘B’ (Rs.)	Angle ‘B’
Food	16,000	123.9°	12,000	99.3°
Clothing	2,500	19.4°	3,000	24.8°
Education	8,000	61.9°	7,000	57.9°
Health	3,000	23.2°	2,500	20.7°
Rent	12,000	92.9°	13,000	107.6°
Miscellaneous	5,000	38.7°	6,000	49.7°
Total	46,500	360°	43,500	360°

Figure (d): Monthly Expenditure of Families ‘A’ and ‘B’ — Two Pie Charts

(e) Based on the table given below, construct a Time Series Line Graph: Line Graph

Year (B.S.)	2077	2078	2079	2080	2081	2082
Per Capita Income (Lakh Rs.)	2.1	2.3	2.5	3.0	2.8	3.3

Scale: Y-axis → 1 unit = 0.5 lakh

Figure (e): Per Capita Income — Time Series Line Graph

(f) The table below shows the contribution of the agricultural sector to Nepal’s GDP in different years. Present this table as a Time Series Line Graph: Line Graph

Fiscal Year	2076/77	2077/78	2078/79	2079/80	2080/81	2081/82
GDP (Billion Rs.)	629	647	662	682	705	728

Scale: Y-axis → 600 to 750 (False line used) | Source: Economic Survey, 2081/82

Figure (f): Agricultural Sector GDP — Time Series Line Graph

(g) The table below shows the expenditure and savings of a family over different years. Based on this, construct a Time Series Line Graph: Multiple Line

Year (B.S.)	2076/77	2077/78	2078/79	2079/80	2080/81	2081/82
Expenditure (Thousand Rs.)	250	270	240	300	315	290
Saving (Thousand Rs.)	20	25	-10	50	55	40

Note: In 2078/79, saving was negative (-10 thousand) → the line falls below the X-axis.

Figure (g): Annual Expenditure and Saving — Multiple Line Graph

The table below shows the share of exports and imports in total trade. Based on this, construct a Time Series Line Graph: Multiple Line

Fiscal Year	2075/76	2076/77	2077/78	2078/79	2079/80	2080/81
Exports (%)	6.4	7.5	8.4	9.4	8.9	8.7
Imports (%)	93.6	92.5	91.6	90.6	91.1	91.3

Figure (h): Share of Exports and Imports — Multiple Line Graph

(i) Based on the data below, construct a Histogram: Histogram

Wages (Thousand Rs.) — Original Data	0–50	0–100	0–150	0–200	0–250
Cumulative Number of Workers	10	15	25	33	40

Converting Cumulative Frequency to Simple Frequency:

Class Interval	Actual Frequency
0–50	10
50–100	5 (15−10)
100–150	10 (25−15)
150–200	8 (33−25)
200–250	7 (40−33)

Figure (i): Wages and Number of Workers — Histogram

(j) The marks obtained by 42 students studying in Class 10 in their second trimester examination in Economics (out of 75 marks) are as follows. Based on this, form a frequency table using a class interval of 10, and then construct a Histogram based on that table: Histogram

Data: 18, 24, 35, 42, 55, 60, 67, 21, 33, 48, 52, 69, 15, 28, 37, 44, 58, 62, 70, 19, 24, 35, 42, 55, 63, 18, 29, 41, 47, 52, 66, 20, 34, 45, 59, 61, 68, 24, 35, 42, 55, 18