Descriptive Statistics

Mean

Median

Variance

Standard Deviation

Skewness

Coefficient of Correlation

Simple Regression

University of Colombo

Institute of Human Recourse Advancement

Individual Assignment

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ABSTRACT

The assignment would be a cushion to learn about the descriptive statistics of mean, median,

variance, standard deviation, skewness, coefficient of correlation and simple regression

model.

I selected a reputed manufacturing company which is one of the fastest growing and largest

conglomerates in Sri Lanka that manufactures and markets many leading brands in biscuits,

confectionery, cereal, organic fruit products and many other categories globally.

“CBL” Ceylon Biscuits Limited, most of people known as “Munchee” which is the largest

confectionery, cereal, organic fruit products, etc company in Sri Lanka. CBL’s export quality

food products have been marketed around the world more than 55 countries through a solid

network of international partners.

INTRODUCTION

Ceylon Biscuits Limited (CBL) is one of the fastest growing and largest FMCG

conglomerates in Sri Lanka that manufactures and markets many leading brands in biscuits,

confectionery, cereal, organic fruit products and many other categories globally.

Vision

“Our vision of becoming the No.1 biscuit, chocolate and confectionary manufacturer and

marketer in Asia, while developing a global presence and recognition.”

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Story Line – In retrospect

Company Name - William’s Biscuit factory

Company Scale - Small scale handmade biscuit venture

Chairman - Mr. Williams

Acquired company - Mr. Simon Arthur Wickramasingha (1939)

Company Name - Williams Confectionery

Employees - 10 Nos.

In 1960 - The Joint Venture with the Sri Lankan Government and CARE

of USA for national welfare

Purpose - Improve the nutritional standard of Sri Lankan children

Factory - Was built in Pannipitiya (1968), Eight acres

Chairman - Mr. Mineka Wickramasingha

In 1980 - CBL expanded to international market by venturing India,

Established CBL Foods

In 2015 - Market leader in all CBL Brands

Company Portfolio

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1. CBL Foods International (Pvt) Ltd

Manufacture - Chocolates, cakes, biscuits, wafers and jelly

Company squire feet - 200,000

2. CBL Natural Foods (Pvt) Ltd

An export oriented company

Manufacture - Natural & certified organic fruit products, cashew nuts and coconut products.

3. Convenience Foods (Lanka) PLC

A largest - Textured soya company

Manufacture - Textured soya nuggets, jelly crystals, instant soup mixes and snacks.

4. Plenty Foods (Pvt) Limited

Manufacturers of Sri Lanka’s most consumed cereal product and herbal porridges made from

100% locally sourced raw material.

5. CBL Exports (Pvt) Ltd

A state-of-the-art manufacturing facility, this company was established at Seethawaka.

Export Processing Zone with the aim of catering to the ever growing global market.

6. CBL Bangladesh (Pvt) Ltd

Ceylon Biscuits Bangladesh (Pvt) Ltd, a wholly owned enterprise of Ceylon Biscuits Limited

was inaugurated in 2014. This is the first Sri Lankan owned confectionery Company in

Bangladesh producing quality Biscuits, Wafers and Chocolate coated biscuits for the large

consumer base of the country.

7. Retail Alliance Limited

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In 2014, CBL introduced Supermarket chain Star United. As of 2014, there were 30

franchised supermarkets within the country.

Brand Portfolio

1. Biscuits

2. Cakes

3. Chocolates

4. Jelly

5. Soy based Products

6. Cereal Products

7. Organic Fruit Products

8. Supermarket Chain

Descriptive Statistics

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According to the manufacturing activities, we expect to identify the relationship between

production capacity and profit ratio. Hence, we selected two variables of production capacity

& profits during last 12 months period to identify the actual relationship.

CBL has been manufacturing several products which are the market leading products &

popular products. Considering the above facts, we have selected a popular chocolate product

named “ Ritzbury Chocolate Fingers” for our calculating activities.

1 st variable – Production of Ritzbury Chocolate Fingers

Month Sales ( 1 Bag = 1000 x 6g packs)January 2016 2,403February 2016 2,736March 2016 1,857April 2016 2,541May 2016 2,493June 2016 2,393July 2016 2,333August 2016 2,285September 2016 2,835October 2016 2,488November 2016 2,602December 2016 2,336∑ x 29,302

Simple Mean

Mean is summation of all observation divided by the number of observation, we call

“Simple mean”. Simple mean denoted by “X”.

= ∑ x

n 6

X = Simple Mean

∑X = Summation of all Observation

n = Number of observation

Then according to the above formulation, we can calculate simple mean (X) as below,

∑ x = 29,302

n = 12

29,302

12

2,441.83

Hence, simple mean value (X) is 2,441.83.

Median

Median is a middle point of the number observation after the arrange Ascending or

Descending order.

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According to above our set of observations, we can calculate the median after arranging the

same in ascending order.

1875, 2285, 2333, 2336, 2393, 2403, 2488, 2493, 2541, 2602, 2736, 2835

Location = (n+1)

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n = Number of Observation

Calculation

n = 12

Location = (12+1) = 6.5

2

Hence, median location of the above data set is 6.5th location.

Median = 2403 + (85*0.5)

= 2403 + 42.5

= 2,445.50

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Variance

We use only absolute value of mean deviation to consider the negative value too .The

purpose of the variance is same. We calculate the square of that difference. Because of this

square answer will stands in a positive. Even though there are negative differences. Therefore

variance is their average of square of the difference between observation and mean. Variance

denoted by “Squire root of simple sigma- σ2 ” and can use the following formulae.

σ2 =

n-1

x = Observation

n = Number of Observation

X 2

2,403 -38.83 1507.772,736 294.17 86535.991,857 -584.83 342026.132,541 99.17 9834.692,493 51.17 2618.372,393 -48.83 2384.372,333 -108.83 11843.972,285 -156.83 24595.652,835 393.17 154582.642,488 46.17 2131.672,602 160.17 25654.432,336 -105.83 11199.99∑ x = 29,302 ∑2 = 674,915.67

σ2 = 674,915.67 = 61,355.97

(12-1) 9

Standard Deviation

Square Root (√) of the variance is called as “Standard deviation”. This is denoted by .

SD = √variance

Hence, standard deviation =√ 61,355.97 = 247.70

Skewness

After construct the frequency curve by using mean, median and Standard deviation create

shape of curve called “Skewness”.

According to the shape of curve, skewness can be categorized in three types.

Positive Skewness

Negative Skewness

Zero skewness

Skewness can construct by using following formulae.

Skewness = 3 (Mean – Median)

Standard Deviation

Calculation

Skewness = 3(2441.83-2445.50)

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247.70

= 3 x -3.67 = - 0.044

247.70

Skewness is (-) value. Therefore, we can decide, Skewness is negative skewness.

2 nd variable – Profit ratio of Ritzbury Chocolate Fingers

Month Profit (Rs.)January 2016 1,081,350February 2016 1,231,200March 2016 835,650April 2016 1,143,450May 2016 1,121,850June 2016 1,076,850July 2016 1,049,850August 2016 1,028,250September 2016 1,275,750October 2016 1,119,600November 2016 1,170,900December 2016 1,051,200∑ x 13,185,900

As we mentioned in 1st Variable, we calculate the followings by using above formulas,

Simple Mean

= ∑ x n = 13,185,900 12

= 1,098,825

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Median

Ascending order,

835650, 1028250, 1049850, 1051200, 1076850, 1081350, 1119600, 1121850, 1143450,

1170900, 1231200, 1275750

Location = (n+1)

2

n = 12

Location = (12+1) = 6.5

2

Hence, median location of the above data set is 6.5th location.

Median = 1,081,350 + (38,250*0.5)

= 1,081,350 + 19,125

= 1,100,475

Variance

X 2 (Mn)1,081,350 -17,475 305.3751,231,200 132,375 17,523.14835,650 -263,175 69,261.0801,143,450 44,625 1,991.3901,121,850 23,025 530.1501,076,850 -21,975 482.9001,049,850 -48,975 2,398.5501,028,250 -70,575 4980.8301,275,750 176,925 31,302.4551,119,600 20,775 431.6001,170,900 72,075 5194.8051,051,200 -47,625 2,268.140∑x = 13,185,900 ∑2 = 136,670.42

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σ2 =

n-1

σ2 = 136,670.42 11 = 12,424.58

Standard Deviation

SD = √variance

Hence, standard deviation =√ 12,424.58 = 111.46

Skewness

Skewness = 3 (Mean – Median)

Standard Deviation

Skewness = 3(1,098,825-1,100,475)

111.46

= 3 x -1,650 = - 44.41

111.46

Skewness is (-) value. Therefore, we can decide, Skewness is negative skewness.

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Coefficient of Correlation

Correlation means relationship between two variables. Consider two variables, one variable is

dependent and other variables are an independent. Considering these two variables must

construct behavior of each variable, depending another variable.

Correlation can categorize as follows,

If Correlation value is positive – Positive Correlation (+)

If Correlation value is negative – Negative Correlation (-)

If no Correlation value – Zero Correlation (0)

Coefficient of correlation is moving between +1 and -1 and this is denoted by “r”.

Considering the variables, we can calculate coefficient of correlation using below formulae,

r = n ∑ xy - ∑ x ∑ y

√(n∑x2 - (∑x)2 (n∑y2 –(∑y)2)

Sales (x) Profit (Rs.) (y) (xy) Mn x2 Mn y2 Mn2,403 1,081,350 2,598.48 5.77 11,693.172,736 1,231,200 3,368.56 7.48 15,158.531,857 835,650 1,551.80 3.44 6,983.102,541 1,143,450 2,905.50 6.45 13,074.772,493 1,121,850 2,796.77 6.21 12,585.472,393 1,076,850 2,576.90 5.72 11,596.052,333 1,049,850 2,449.30 5.44 11,021.85

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2,285 1,028,250 2,349.55 5.22 10,572.982,835 1,275,750 3,616.75 8.03 16,275.382,488 1,119,600 2,785.56 6.19 12,535.042,602 1,170,900 3,046.68 6.77 13,710.062,336 1,051,200 2,455.60 5.45 11,050.2129,302 13,185,900 32501.45 72.17 146,256.61r = n ∑ xy - ∑ x ∑ y

√(n∑x2 - (∑x)2 (n∑y2 –(∑y)2)

=12 x 32,501,450,000 –(29,302 x 13,185,900)

√ (12 x 72,170,000)-(72,170,000)2 (12 x 146,256,610,000 – 13,185,9002)

= 390,017,400,000 -386,373,241,800

√866,040,000-5,208,508,900,000,000 (1,755,079,320,000-173,867,958,800,000)

= 3,644,158,200

√-52,085,080,340,000,000 (-172,112,879,500,000)

= 3,644,158,200

39,279,869,810,000,000,000,000

= 9.27 x 10 -14

“r” value stands at r > -0.5. Hence, this is a Weak Positive Correlation.

Regression Model

After calculating regression value, we can construct the regression model to identify the

relationship between two variables. It can show graphically. That is called “Scatter

Diagram”. By using scatter diagram, we could construct a linear line and we called “Line of

Best Fit”. Line of Best Fit can be identified as “Regression Model”.

Regression models can be basically specified as follows,.

Simple Regression Model

Multiple Regression Model

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Simple Regression model for two variables by using following equations.

1st Equation;

2nd Equation;

Data for Equation 01

13,185,900 = 12a + 29,302b ------------(1)

Data for Equation 02

32,501,450,000 = 29,302a + 72,170,000b ------------- (2)

1st equation x 2441

32,186,781,900= 29,302a+29,302b ----------------(3)

2 – 3

32,501,450,000 - 32,186,781,900 = 29,302a + 72,170,000b -29,302a-29,302b

314,668,100 = 72,140,698b

b = 314,668,100

72,140,698

b = 4.36

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a value

13,185,900 = 12a + 29,302b

13,185,900 = 12a + 127,756.72

12a =13,185,900 -127,756.72

12a = 13,058,143.28

a =1,088,178.60

Regression model,

y = 1,088,178 + 4.36x

We considered “a” value in Millions. Hence, a = 1.08

y = 1.08 + 4.36x

Considering the above equation,

y = Profit

x = Sales

Profit ratio = 1.08 + 4.36 x (Sales )

Then, If x = 0,

y = 1.08 + 4.36 = 5.44

We considered sales figure in 000’ for our calculations.

Then,

If, x=100

y = 1.08 + 4.36 x 100 = 437.08

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We can calculate the variation of profit by substitute values of sales.

Now can construct the Regression model using above “x” and “y” value.

Sales ( 000') Profit (Mn)50 219

100 437150 655200 873250 1091300 1309350 1527400 1745450 1963500 2181

As per the above figures, we construct the linear line as “ Line of Best Fit” and according

to above line regression model can show as follows for the above two variables.

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Conclusion

Considering above Regression model we can build up following conclusion regarding

relationship and behavior of above two variables.

Increasing of sales mainly affected to the profit and towards enhancement of sales, the

profit ratio is increasing in enhanced levels.

It’s however, we should concern about the sales & production capacity of the factory

since such forecasted sale should be manufactured by the company during targeted time

period and also they would be able to facilitate their storage capacity.

Recommendation

Recommendation is to enhance the sales turnover in a considerable amount since we should

be able to control the market demand and supply. In addition to that we have to enhance the

factory manufacturing capacity & storage facilities towards such enhancement of sales.

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REFERENCE

Data of sales and other details - Manuka Weerasekara – Sales Executive of CBL

Though internet

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