BUSINESS STATISTICSGURU NANAK COLLEGE

SYLLABUS

INRODUCTION OF BUSINESS STATISTICS-DEFINITION-VARIABLES-QUALITATIVE AND

QUANTITATIVE DATA’S-PRIMARY AND SECONDARY DATA’S-COLLECTION OF DATA’S-CENSUS

METHODS-SAMPLING METHODS-PRECAUTIOUS BY USING SECONDARY DATA.

CLASSIFICATION AND PRESENTATION OF DATA’S-TABULATION-FREQUENCY DISTRIBUTION-

DIAGRAMS AND GRAPHICAL REPRESENTATION OF DATA’S-BAR DIAGRAMS-PIE DIAGRAMS-FREQUENCY

CURVES-OGIVE CURVES-HISTOGRAM-POLYGON-LORENZ CURVE.

MEASURES OF CENTRAL TENDENCY-MEAN-MEDIAN AND-MODE-MEASURE OF VARIATION-

RANGE-QUARTILE DEVIATION, STANDARD DEVIATION, MEAN DEVIATION AND COEFFICIENT-

CHARACTERISTICS-USES AND LIMITATIONS ADVANTAGES- DISADVANTAGES.

UNIT – 1

UNIT – 2

UNIT - 3

SYLLABUS

SKEWNESS TYPES AND MEASUREMENTS-KARL PEARSON-BOWLEY

TIME SERIES-COMPONENTS-MODELS, TREND MEASUREMENTS (GRAPHIC AND STRAIGHT LINE

METHOD) SEASONAL INDEX MEASUREMENTS-SIMPLE AVERAGE AND MOVING AVERAGE METHOD

REFERENCE:

S.B. GUPTA – SULTAN CHAND

V.R. VICTOR – MARGHAM PUBLICATIONS

UNIT – 4

UNIT – 5

BUSINESS STATISTICS

FOR EXAMPLE:

Statistics is an imposing form of mathematics whereas suggest tables,

charts, and figures which is found in newspapers, journal's, books,

radio and lectures etc.,

BUSINESS STATISTICS

There are 932 females for every 1000 males in india.

Whereas in russia, there are 1170 females per 1000 males. These statements contains

figures and they may be called as numerical statements of facts. They are highly

convenient form of communication. At the same time they are clear precise and

meaningful.

Facts and figures related to population, production, national income, profit, sales, births

and deaths etc., are all connected with statistics.

Statistics refers to quantitative information.

MEASURES OF CENTRAL TENDENCY OR

AVERAGES

CENTRAL TENDENCY OR AVERAGES

Objectives of statistical analysis is to get one single value that describes the

characteristics of the entire mass of data's. Such value is called central value or

average.

FOR EXAMPLE:

Average height or life of an indian, average income, average marks

and average sales etc.,

MEAN OR ARITHEMATIC MEAN

MEAN OR ARITHEMATIC MEAN

Count the number of times a particular value

is repeated is called the frequency of that

class

a) Individual observation

b) Discrete series

c) Continuous series

FREQUENCY DISTRIBUTION

SUM NO:1- THE MARKS OBTAINED BY 25 STUDENTS A CLASS

10 20 20 30 40 25 25 30 40 20 25 25 50 15 25 30 40

50 40 50 30 25 25 15 40

MARKS (X) TALLY BARS FREQUENCY

10

15

20

25

30

40

50

I

II

III

IIII II

IIII

IIII

III

1

2

3

7

4

5

3

N = 25

SUM NO: 2 – THE WEEKLY WAGES PAID TO 30 WORKERS IN A FACTORY GIVEN

BELOW. CALCULATE FREQUENCY TABLE.

3000 3500 2000 3000 2250 2000 2000 3000 2250 2000 3000 2250

3000 2250 2000 3000 2250 2000 3000 3000 2250 3000 2000 2000

3000 2250 3500 3000 2000 2250

WAGES (X) TALLY BARS FREQUENCY

2000

2250

3000

3500

IIII IIII

IIII III

IIII IIII I

II

9

8

11

2

N = 30

I. MEAN OR ARITHMETIC MEAN

a) INDIVIDUAL OBSERVATION

N = Total Frequency

b) DISCRETE SERIES

C) CONTINUOUS SERIES

𝑋 =𝛴𝑓𝑚

𝑁

𝑋 = 𝐴 +𝛴𝑓𝑑

𝛴𝑓 SHORT CUT METHOD

SUM NO: 1- FOLLOWING TABLES GIVES A MARKS OBTAINED BY 10

STUDENTS IN A CLASS. CALCULATE ARITHMETIC MEAN (AM)

X 40 50 30 60 70 80 40 50 60 90

X

40

50

30

60

70

80

40

50

60

90

Σx =570

𝑋 =570

10= 57

𝑋 = 57

a) INDIVIDUAL OBSERVATION

SUM NO: 2- CALCULATE ARITHMETIC MEAN FROM THE FOLLOWING DATA.

FIND THE ARITHMETIC MEAN .

MARKS 20 30 40 50 60 70

X

20

30

40

50

60

70

Σx = 270

𝑋 =𝛴𝑋

𝑁

𝑋 = 270

6= 45

𝑋 = 45

SUM NO: 1- FROM THE FOLLOWING DATA OF MARKS, OBTAIN BY 60 STUDENTS

OF A CLASS. CALCULATE THE AVERAGE MARKS.

b) DISCRETE SERIES

MARKS 20 30 40 50 60 70

NO.OF.

STUDENTS

8 12 20 10 6 4

MARKS

(X)

NO. OF.

STUDENT (F)

FX

20 8 160

30 12 360

40 20 800

50 10 500

60 6 360

70 4 280

Σ(F) = 60 ΣF(X) = 2460

𝑋 = 𝛴𝑓(𝑋)

𝑁 =

2460

60 = 41

𝑋 = 41

SUM NO: 1 - SHORT CUT METHOD:

MARKS

(X)

NO. OF.

STUDENT

(F)

dA = 40

(X-A) fd

20 8 -20 -160

30 12 -10 -120

40 20 0 0

50 10 10 100

60 6 20 120

70 4 30 120

Σ(F) = 60 Σfd= 60

𝑋 = 40 + 60

60 = 41

SUM NO: 1 – FROM THE FOLLOWING DATA OF MARKS. OBTAIN CALCULATE

ARITHMETIC UNDER DIRECT METHOD. FIND M.

c) CONTINUOUS SERIES

MARKS (X) N0. OF.

STUDENTS

(f)

m fm

0-10 5 5 25

10-20 10 15 150

20-30 25 25 625

30-40 30 35 1050

40-50 20 45 900

50-60 10 55 550

Σ(f) = 100 Σfm=3300

MARKS 0-10 10-20 20-30 30-40 40-50 50-60

NO. OF.

STUDENTS

5 10 25 30 20 10

𝑋 = 3300

100 = 33

𝑋 = 33

SUM NO: 1- SHORT CUT METHOD

MARKS

(X)

N0. OF.

STUDENTS

(f)

m M-AA = 25

fd

0-10 5 5 -20 -100

10-20 10 15 -10 -100

20-30 25 25 0 0

30-40 30 35 10 300

40-50 20 45 20 400

50-60 10 55 30 300

Σ(f) = 100 Σfd = 800

𝑋 = 25 + 800

100 = 33

𝑋 = 33

SUM NO: 2 – CALCULATE ARITHMETIC MEAN FROM THE FOLLOWING DATA.

FIND M.

MARKS 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80

FREQUENCY 4 6 5 10 5 5 10 20

MARKS (F) m fm0-10 4 5 20

10-20 6 15 90

20-30 5 25 125

30-40 10 35 350

40-50 5 45 225

50-60 5 55 275

60-70 10 65 650

70-80 20 75 1500

Σ(f)= 65 Σ(fm)=3235

𝑋 = 3235

65= 49.76

𝑋 = 49.76

SUM NO: 3 – CALCULATE ARITHMETIC MEAN UNDER STEP DEVIATION

METHOD.

CLASS

LIMITS

0-10 10-20 20-30 30-40 40-50 50-60

FREQUENCY 5 10 25 30 20 10

CLASS

LIMITS f m d

(m-a/c)

fd

0-10 5 5 -2 -10

10-20 10 15 -1 -10

20-30 25 25 0 0

30-40 30 35 1 30

40-50 20 45 2 40

50-60 10 55 3 50

N= 100 Σ(fd)= 80

𝑋 = 25 + 80

100 × 10

𝑋 = 25 + 8 𝑋 = 33

𝑋 = A + 𝛴𝑓𝑑

Σf × 𝐶

SUM NO: 4 – FROM THE FOLLOWING DATA CALCULATE THE ARITHMETIC MEAN

DATA.

MARKS BELOW 10 BELOW 20 BELOW 30 BELOW 40 BELOW 50 BELOW 60 BELOW 70 BELOW 80

NO. OF.

STUDENTS

15 35 60 84 96 127 198 250

MARKS NO. OF.

STUDENTSsf m d

(m-a/c)

fd

0-10 15 15 5 -3 -45

10-20 35 20 15 -2 -40

20-30 60 25 25 -1 -25

30-40 84 24 35 0 0

40-50 96 12 45 1 12

50-60 127 31 55 2 62

60-70 198 71 65 3 213

70-80 250 52 75 4 208

Σ(f)=250 Σ(d)= 4 Σ(fd=385

𝑋 = A + 𝛴𝑓𝑑

Σf × 𝐶

𝑋 = 35 + 385

250 × 10

𝑋 = 35 + 15.4 𝑋 = 50 . 4

II. MEDIAN

MEDIAN

SUM NO: 1 – CALCULATE THE MEDIAN FROM THE FOLLOWING DATA, THE CLASS

INTERVALS ARE UNEQUAL.

MARKS 0-10 10-30 30-60 60-80 80-90

FREQUENCY 5 15 30 8 2

MARKS FREQUENCY CUMULATIVE

FREQUENCY

(CF)

0-10 5 5

10-20 7.5 12.5

20-30 7.5 20.0 (PCF)

30-40 10 30.0

40-50 10 40.0

50-60 10 50.0

60-70 4 54.0

70-80 4 58.0

80-90 2 60.0

N = 60

20 N = 30

Median = 30 + 30 − 20.0

10 × 10

Median = 30 + 10

10 × 10 Median = 40

SUM NO: 2 – FIND THE MEDIAN FROM THE FOLLOWING CLASS INTERVALUES.

WAGES 60-69 70-79 80-89 90-99 100-109 109-119

FREQUENCY 5 15 20 30 20 8

WAGES C.I FREQUENCY CUMULATIVE

FREQUENCY

60-69 59.5-69.5 5 5

70-79 69.5-79.5 15 20

80-89 79.5-89.5 20 40 (PCF)

90-99 89.5-99.5 30 70

100-109 99.5-100.5 20 90

110-119 100.5-109.5 8 98

N = 98 N = 323

𝑁

2 =

98

2 = 49

Median = 89 . 5 + 49 − 40

30 × 10 = 92 . 5

Median = 92 . 5

III. MODE

MODE Mode is the measure of central value. It is the value which

has the maximum frequency. In case of frequency

distribution of an continuous variable mode is obtained by

giving weights to the frequency of modal class, then pre

modal and post modal class.

SUM NO: 1 – FIND MODE FROM THE FOLLOWING GIVEN DATA.

110 120 130 120 110 140 130 120 140 120

a) INDIVIDUAL OBSERVATION

X TALLY BAR f

110 I I 2

120 I I I I 4

130 I I 2

140 I I 2

Mode = 120

SUM NO: 1 – CALCULATE MODE FROM THE FOLLOWING DATA.

b) DISCRETE SERIES

SIZE 28 29 30 31 32 33

NO. OF.

PERSONS

10 20 40 65 50 15

SIZE NO. OF.

PERSONS

28 10

29 20

30 40

31 65

32 50

33 15

Mode = 31

SUM NO: 1 – CALCULATE MODE FROM THE FOLLOWING DATA.

c) CONTINUOUS SERIES

SALES BELOW - 60 BELOW - 62 BELOW - 64 BELOW - 66 BELOW - 68 BELOW- 70 BELOW - 72

FREQUENCY 12 18 25 30 10 3 2

SALES (X) f

58-60 12

60-62 18

62-64 25 (f0)

64-66 30 (f1)

66-68 10 (f2)

68-70 3

70-72 2

Mode = 64 + 30 − 25

2 30 − ( 25 + 10 ) × 2

Mode = 64 . 4