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# Mean, median, mode, Standard deviation for grouped data for Statistical Measure for Shampoo in Indian market

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Detail Survey on Indian manufacture shampoo for management statistical purpose and calculation of Mean, median, mode, Standard deviation for grouped data for Statistical Measure for Shampoo in Indian market

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### Mean, median, mode, Standard deviation for grouped data for Statistical Measure for Shampoo in Indian market

1. 1. Managerial Statics Mean, median, mode, Standard deviation for grouped data for Statistical Measure for Shampoo in Indian market Presented to Sameer Virani By Renzil D’cruz http://RenzilDe.com http://about.me/renzilde http://linkedin.com/in/renzilde 1
2. 2. Managerial Statics Introduction In statistics and data analysis, the mean, median, mode, range, and standard deviation tell researchers how the data is distributed. Each of the five measures can be calculated with simple arithmetic formulae. The mean and median indicate the "centre" of the data points. The mode is the value or values that occur most frequently. Range is the span between the smallest value and largest value. Standard deviation measures how far the data "deviates" from the centre, on average. Knowing how to calculate these statistical measures will help you analyze data from surveys. We have conducted survey on sample of 50 people age group between 18-25, who are consumers of various Shampoos. We compare Sunsilk, L’Oreal with respect to other brands on various factors. In questionnaire, we compare various shampoos on 10 features such as price, size, aroma etc. For which we have got good response from our Classmates, friends and family members. The shampoo market in India is estimated to be 2,500-3,000 crore. The shampoo market is India is categorized according to the benefits they provide. Mostly consisting of three kinds of shampoos cosmetic, herbal and anti dandruff, the shampoo market in India has managed to tap users of the various segments according to their requirements and preferences. Due to the continuous efforts of the top shampoo brands in India penetration of shampoos in urban areas is almost 100%. As far as penetration of shampoo in the rural areas is concerned it has risen by almost 18% in the current scenario. The top shampoo brands in India include Sunsilk, Clinic Plus, L’oreal and Pantene. The company that leads the shampoo market in India is Hindustan Unilever Limited. The top three most sought after brands Sunsilk, Dove and Clinic are produced by HUL. The company holds a 44% market share in the Indian shampoo industry. It is said that HUL earns almost 8% of its revenue from the sale of these products. Proctor and Gamble the second top shampoo brand in India holds a market share of around 25% in the Indian shampoo industry. The revenue earned from the value of shampoos from Proctor and gamble is almost 17%. 2
3. 3. Managerial Statics Various Shampoos in Indian Market: Sunsilk: Sunsilk is a hair care brand, primarily aimed at women, produced by the Unilever group, which is now considered the world's leading company in hair conditioning and the second largest in shampoo. Sunsilk is Unilever’s leading hair care brand, and ranks as one of the Anglo-Dutch conglomerate's “billion dollar brands". Sunsilk shampoos, conditioners and other hair care products are sold in 69 countries worldwide. Sunsilk is sold under a variety of different names in markets around the world including Elidor, Seda and Sedal. The brand is strongest in Asia, Latin America and the Middle East and is the number one hair care brand in India, Brazil, Argentina, Bolivia, Bangladesh, Sri Lanka and Thailand L’oreal: The L'Oréal Group is the world's largest cosmetics and beauty company with its registered office in Paris and head office in the Paris suburb of Clichy, Hautsde-Seine, France, it has developed activities in the field of cosmetics. Concentrating on hair colour, skin care, sun protection, makeup, perfumes and hair care, the company is active in the dermatological, tissue engineering and pharmaceutical fields and is the top nanotechnology patentholder in the United States. L'Oréal is a listed company, but the founder's daughter Liliane Bettencourt and the Swiss food company Nestlé each control around 30 percent of the shares and voting rights. Questionnaire For Shampoo Survey: Please rate the following on the scale of 1-7:(1:Lowest & 7: Highest) Company SUNSILK (HUL) LOREAL Variable Price Availability Aroma Packaging Varieties Value For Money Brand Ambassadors Advertising Satisfaction 3 VATIKA (DABUR)
4. 4. Managerial Statics Price 30 25 20 Sunsilk 15 L'oreal Others 10 5 0 1 2 3 4 5 6 7 Availability 25 20 15 Sunsilk L'oreal 10 Others 5 0 1 2 3 4 5 6 4 7
5. 5. Managerial Statics Aroma 20 18 16 14 12 Sunsilk 10 L'oreal 8 Others 6 4 2 0 1 2 3 4 5 6 7 Quality 16 14 12 10 Sunsilk 8 L'oreal 6 Others 4 2 0 1 2 3 4 5 6 5 7
6. 6. Managerial Statics Packaging 18 16 14 12 10 Sunsilk 8 L'oreal 6 Others 4 2 0 1 2 3 4 5 6 7 Varieties 20 18 16 14 12 Sunsilk 10 L'oreal 8 Others 6 4 2 0 1 2 3 4 5 6 6 7
7. 7. Managerial Statics Value for money 18 16 14 12 10 Sunsilk 8 L'oreal 6 Others 4 2 0 1 2 3 4 5 6 7 Brand Ambassador 20 18 16 14 12 Sunsilk 10 L'oreal 8 Others 6 4 2 0 1 2 3 4 5 6 7 7
8. 8. Managerial Statics Advertising 18 16 14 12 10 Sunsilk 8 L'oreal 6 Others 4 2 0 1 2 3 4 5 6 7 Satisfaction 25 20 15 Sunsilk L'oreal 10 Others 5 0 1 2 3 4 5 6 8 7
9. 9. Managerial Statics Mean: The arithmetic mean or average of a set of numbers is the expected value. The mean is calculated by adding up all the values, and then dividing that sum by the number of values. Mean (x)=A+(Σ(fd)/n)*i Median: The median is the middle value in a set of values. To find the median, order the numbers from largest to smallest, and then choose the value in the middle. Median =L+((n/2-PCF)/f)*i Mode: The mode of a set is the value or values that occur most frequently. There can be more than one mode in a set. If there is more than one mode, you simply list all of the modes; you do not have to average them. Mode=L+{∆1/(∆1+ ∆2)}*i 60 50 40 Mean 30 Median Mode 20 10 0 Sunsilk L'Oreal Other 9
10. 10. Managerial Statics Standard Deviation: It is a measure of how much spread or variability is present in the sample. If all the number in the sample are very close to each other in such cases SD is zero (0) and if the numbers are well dispersed than SD tends to be large. It is calculated as: Standard deviation (σ) = *i STANDARD DEVIATION 16 14 12 10 8 6 4 2 0 SUNSILK LO'REAL OTHERS Quartile: The quartiles of a set of values are the three points that divide the data set into four equal groups, each representing a fourth of the population being sampled For group data the formula is: Q1 can be given as (L+ n/4 – pcf x i )/f Q3can be given as (L+3 n/4 – pcf x i )/f Inter-quartile Deviation: In descriptive statistics, the Inter-quartile Deviation, also called the midspread or middle fifty, is a measure of statistical dispersion, being equal to the difference between the upper and lower quartiles. Inter-quartile Deviation = Q3 − Q1 10
11. 11. Managerial Statics Skewness It is a measure of the asymmetry of the probability distribution of a real-valued random variable. The skewness value can be positive or negative, or even undefined. Qualitatively, a negative skew indicates that the tail on the left side of the probability density function is longer than the right side and the bulk of the valueslie to the right of the mean. A positive skew indicates that the tail on the right side is longer than the left side and the bulk of the values lie to the left of the mean. A zero value indicates that the values are relatively evenly distributed on both sides of the mean, typically implying a symmetric distribution. SKEWNESS 0.1 0.05 0 -0.05 SUNSILK LO'REAL OTHERS -0.1 -0.15 -0.2 -0.25 Coefficient of quartile deviation: It is the simple method of studying variation. it is defined as the difference between the value of the smallest and the highest observation. the relative measure corresponding to deviation is called coefficient of quartile deviation t is given by, Coefficient of quartile deviation =(Q3 − Q1)/( Q3 + Q1) 11
12. 12. Managerial Statics CO-EFFICEINT OF Q.D 0.3 0.25 0.2 0.15 0.1 0.05 0 SUNSILK LO'REAL OTHERS AVERAGE DEVIATION 20 18 16 14 12 10 8 6 4 2 0 SUNSILK LO'REAL OTHERS SUNSILK: Analysis Mean Median Mode Parameters Price Availability 212 24.2 205.56 26 Standard Quartile Coefficient Skewness Average deviation Deviation of Quartile Deviation deviation 182.76 22.91 100.53 0.39 1.27 55.52 27.38 7.05 8.37 0.16 -0.45 5.50 12
13. 13. Managerial Statics Aroma Quality Packaging Varieties Value for Money Brand Ambassador Advertising Satisfaction 22.3 20.8 22.1 24.3 19.9 22.63 20.77 22.31 26.32 20.88 22.75 19.29 25.88 28.09 22.5 6.4 6.45 5.47 7.28 5.32 8.32 9.43 9.92 10.55 9.81 0.18 0.22 0.22 0.22 0.25 -0.07 0.23 -0.69 -0.52 -0.499 4.68 5.31 4.49 6.04 5.51 22.9 24.23 26.39 9.12 8.04 0.17 -0.38 4.65 22.1 21.4 25.66 21.5 28.13 21.84 6.62 5.73 10.12 7.12 0.20 0.17 -0.91 -0.01 6.53 4.46 LOREAL: Analysis Parameters Price Availability Aroma Quality Packaging Varieties Value for Money Brand Ambassador Advertising Satisfaction Mean Median Mode Skewness Average Deviation 298 20.4 20.1 25.2 23.1 22.7 21.6 322 22 19.66 26.66 23.52 23.5 21.76 Standard Quartile Coefficient Deviation Deviation of Quartile Deviation 331.08 73.63 84.5 0.14 24.16 7.62 12.18 0.30 19.09 7.22 3.92 0.89 30 7.08 10 0.19 23.66 8.73 8.3 0.17 27.5 7.54 12.01 0.26 20.71 5.89 8.46 0.19 -0.45 -0.49 0.14 -0.68 -0.06 -0.64 0.15 62.34 6.40 5.90 5.76 4.92 6.22 4.72 23.6 25.33 27.14 7.9 9.29 0.24 -0.44 6.26 23.7 22.6 25 22.08 18.75 13.5 7.26 9.6 10.85 9.17 0.23 0.19 0.68 0.95 6 5.31 OTHERS: Analysis Parameters Mean Median Mode Standard Quartile Coefficient Skewnwess Average Deviation Deviation of Quartile Deviation Deviation 13
14. 14. Managerial Statics Price Availability Aroma Quality Packaging Varieties Value for Money Brand Ambassador Advertising Satisfaction 216 18.7 18 18.6 17.2 17 18 209.09 17.73 18.21 19 11.25 14.72 18.13 234.21 13.75 18.33 17 14.38 13.09 18.33 64.57 7.97 7.5 7.16 8.21 7.23 6.14 95.47 11.85 9.88 9.01 11.57 9.82 8.75 0.22 0.32 0.27 0.24 0.34 0.30 0.24 -0.28 0.62 -0.04 0.22 0.34 0.54 -0.05 53.72 62.4 5.8 5.63 6.54 5.88 4.62 17.7 18.07 20.83 7.28 3.17 0.08 -0.43 5.93 18.4 16.9 17.5 16.25 16.25 15 6.61 0.6 8.6 2.5 0.24 0.05 0.33 3.17 5.19 16.82 THE MARKET SHARES BRANDS SHARE % SUNSILK 20 CLINIC 25 L’Oreal 5.5 PANTENE 11 HALO 3.4 OPTIMA 3.6 LAKME 1 ULTRA DOUX 1.2 14