1. Measures of Central Tendency (Contd…) Prepared by: Bhakti Joshi Date: November 28, 2011

2. Frequency distribution of Weights in Pounds of a sample of packages Weights Class Frequency of packages (f) Mid-point (x)fx 10.0 – 10.9 1(10+10.9)/2= 10.51*10.5= 10.5 11.0 – 11.9 411.54*11.5= 46 12.0 – 12.9 612.56*12.5=75 13.0 – 13.9 813.58*13.5= 108 14.0 – 14.9 1214.512*14.5= 174 15.0 – 15.9 1115.511*15.5=170.5 16.0 – 16.9 816.58*16.5=132 17.0 – 17.9 717.57*17.5=122.5 18.0 – 18.9 618.56*18.5=111 19.0 – 19.9 219.52*19.5=39 65 988.5 15.2

3. Monthly Average Cash Balances of 600 customers Class (Rupees) Frequency of Customers (f) Mid-point (x)fx 0 – 49.9 78(0+49.9)/2= 2578*25= 1950 50.00 - 99.99 123759225 100.00 - 149.99 18712523375 150.00 - 199.99 8217514350 200.00 – 249.99 5122511475 250.00 – 299.99 4727512925 300.00 - 349.99 133254225 350.00 – 399.99 93753375 400.00 – 449.99 64252550 450.00 – 499.99 44751900 600 85,350 142.25

4. Median …Central Item of a data set (N+1) /2 = M N = Number of observations M= Median

5. Median Age Intervals Frequency of Mobile Phones Owned (f) Cumulative Frequency 10 - 1520 15 - 204060 20 - 2560120 25 - 3070190 30 - 3560250 35 - 4030280 40 - 4520300 Interpretation?

6. Estimated median weight of the fish caught Weights Intervals Frequency of fish caught (f) Cumulative Frequency 10-19.588 20-29.51523 30-39.52346 40-49.53783 50-59.546129 60-69.552181 70-79.584265 80-89.597362 90-99.516378 100-109.55383 Item or number that represents median 383+1 / 2= 192 nd item Class that contains the median item 70 – 79.5 Width of the weights interval 9.5 Estimated median value? (192 – (181+1) 84 * 9.5 + 70 = 71.13

7. Mode …Value that is repeated most often in the data set. Mode is not used for ungrouped data Age Intervals Frequency of Mobile Phones Owned (f) Cumulative Frequency 10 - 1520 15 - 204060 20 - 2560120 25 - 3070190 30 - 3560250 35 - 4030280 40 - 4520300 Interpretation?

8. Relationship between Mean-Median- Mode Mean < Median < Mode = Positively Skewed Mean> Median> Mode = Negatively Skewed Mean = Median = Mode = Normal

9. Positively (right) Skewed Negatively (left) Skewed Normal

10. Projects Stock Prices of Companies representing any one of the following industries listed on the BSE or NSE Textiles Banking Automobiles IT/Telecommunication Pharmaceutical Foods & Beverages Infrastructure Steel Oil & Gas Chemicals

11. Project Requirements Select 2 or more stocks of representative industry Stock prices of minimum 100 data points each Background of the representative companies – Names – Industry – Occupation (Trading, manufacturing, distribution, etc) – Products/services – Customers Select statistical tools to compare and analyze the trends and performance of the stocks in the stock market

12. Email: bhaktij@gmail.com Website: www.headscratchingnotes.netbhaktij@gmail.comwww.headscratchingnotes.net

13. Frequency and Distribution Curve

14. Geometric Mean