Basic Statistics II

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Reading a Histogram

Example 9. The following histogram shows the monthly wages (in rupees) of workers in a factory

Let us explain it with the help of an example

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i. Find the maximum number of workers getting a wage.ii. Find the least wage and highest wage with no. of workers

earning themiii. How many workers get a monthly wage of Rs. 8000 or

less ?

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iii. 50 workers get a wage of Rs 8000 or less asRs (4000 – 5000) – 4 workersRs (5000 – 6000) – 10 workersRs (6000 – 7000) – 12 workersRs (7000 – 8000) – 24 workersTotal – 50

ii. The least wage is between Rs (4000 – 5000) and 4 workers are getting that. The corresponding figures for highest wage are Rs (9000 – 10000) and four workers get that

i. The maximum number of workers is 25 getting wages between Rs (7000 – 8000).

Solution :

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iv. What is a cumulative frequency (Ogive)?

The cumulative frequency, also known as an Ogive, is another way to analyze the frequency distribution table. Unlike a frequency distribution which tells you how many data points are within each class, a cumulative frequency tells you how many are less than or within each of the class limits.

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Compute the cumulative frequency /Ogives for the following data:

Example -10

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Frequency distribution table with cumulative frequency (Ogive)

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0 1 2 3 4 5 6 70

5

10

15

20

25

30

cumulative distribution chart

Series1

Class number

umila

tive

Freq

uenc

y

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Draw a ogive curve for the following data:

Example-11

Marks Frequency Ogive

0-10 2

10-20 8

20-30 12

30-40 18

40-50 28

50-60 22

60-70 6

70-80 4

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Marks Frequency Cumulative Frequency

0-10 2 2

10-20 8 10

20-30 12 22

30-40 18 40

40-50 28 68

50-60 22 90

60-70 6 96

70-80 4 100

Solution

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i. We plot the points with coordinates having abscissae as actual limits and ordinates as the cumulative frequencies, (10, 2), (20, 10), (30, 22), (40, 40), (50, 68), (60, 90), (70, 96) and (80, 100) are the coordinates of the points.

ii. Join the points plotted by a smooth curve.

iii. An Ogive is connected to a point on the X-axis representing the actual lower limit of the first class.

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X -axis 1 cm = 10 marks, Y -axis 1cm = 10 c.f.

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Using the data given below, construct a cumulative frequency table and draw the Ogive.

Example- 12

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cumulative frequency table

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To Plot an Ogive

iii. An Ogive is connected to a point on the X-axis representing the actual upper limit of the last class [in this case) i.e., point (80.5, 0)].

i. We plot the points with coordinates having abscissae as actual lower limits and ordinates as the cumulative frequencies, (70.5, 2), (60.5, 7), (50.5, 13), (40.5, 23), (30.5, 37), (20.5, 49), (10.5, 57), (0.5, 60) are the coordinates of the points.

ii. Join the points by a smooth curve.

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X-axis 1 cm = 10 marksY-axis 2 cm = 10 c.f

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http://www.nos.org/Secmathcour/eng/ch-28.pdf

www.pdfchm.com www.chmpdf.com

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Pie Diagram or Pie Chart

It is also known as angular diagram. It is used to represent percentage break downs of the given data. For example, the exports of a country to different countries and continents of the world can be expressed into ratios or percentages.

These ratios or percentages can then be converted into angles by the formula

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Steps in the construction of Pie diagram

i. Find the total of all components.

ii. Find ratio or percentage of the share of sub-division to the total and multiply by 360° to get the angle corresponding to each sub-division.

iii. Draw a circle of a suitable size.

iv. Use protractor to draw different angles at the centre. Preferably start with the largest one.

v. Shade the different segments with different colours or shades.

vi. Write the components with percentage values in the marked, shaded or coloured areas.

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Example-11

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Draw the Pie diagram for the following data

Country Area (km²) Pre Ang

Austria 83858

Denmark 43094

Finland 336593

Germany 357022

Greece 131940

Italy 301230

Sweden 449964

United Kingdom 244820

Total 100 360

Example-12

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Country Area (km²) Percentage (100%) Degree

Austria 83858 4.30 15.49

Denmark 43094 2.21 7.96

Finland 336593 17.27 2.19

Germany 357022 18.32 65.96

Greece 131940 6.77 24.38

Italy 301230 15.46 55.65

Sweden 449964 23.09 83.13

United Kingdom 244820 12.56 45.23

Total 1948521 100 360

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4%2%

17%

18%

7%15%

23%

13%

Pie diagram of representing the area

12345678

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Introduction to Statistics