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Histograms Organize data into groups by counting how much data is in each group Groups Bins Frequency number of observations Max = maximum value of the given data Min= minimum value of the given data Range=Max-Min

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Histograms Bin width=(max-min)/# of bins Adjusted bin width=round up the bin width to the higher value Eg: if bin width is 5.4, the adjusted bin width 6 if bin width is 0.028, the adjusted bin width 0.03 Number of bins to use- when dealing with a lot of data, use between 8 and 16 bins

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Histogram

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Example 1 The Table gives the estimated gross income in millions of dollars for the 40 highest paid entertainers in 1995 and 1996 combined. 1.Calculate the following for the data a)Maximum b) Minimum c)Range d)Bin Width e) Adjusted bin width 2.Create Table I 3.Create Histogram

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Example 1- Raw data 130314344 5159507733 2546904030 3240563350 6375357442 3144285936 63442848171 33283615042

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Table 1(First 3 bins) Bin limits FrequencyRelative Frequency 25 10.025 35 110.275 45 110.275 Bin 1- (0,25] Bin 2- (25,35] Bin 3- (35,45] These two columns will generated automatically by excel This column has to entered manually Min/if you have decimals for min, a number higher than min of raw data

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Table 1(contd./Last 4 bins) Bin limits FrequencyRelative Frequency 145 00 155 10.025 165 00 175 10.025 Bin 13 –(135,145] Bin 14- (145,155] Bin 15- (155,165] Bin 16- (165,175] We select the number of bins such that it captures the max of raw data

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Creating Histogram Enter your Raw data into excel Enter your Bin limits into excel Tool->Data analysis->Histogram Input range- Enter the cells which contain the raw data Bin range- Enter the cells which contain bin limits Output range- Enter the cell you want to have the output You should now get two columns generated by the histogram function (bin limits and frequency) Insert->chart->standard type->column->next Data range tab->enter data range(select the data created by excel-the two columns without the labels) In the same window Series tab->enter values(select the data on frequency column-without the label)-> enter the category (x)-axis labels(select the data on bin limits column-without the label) Now select the data series->right click->format data series->select options tab->make the gap width to 0 Now enter appropriate Title/name the axis (using chart options)

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Project Focus You must save the data file you download from the yahoo website as “.xls” (when you save it initially it will save the file as “.csv”) Create a new column of Ratios of Closes, Where (gives us information about how two consecutive week’s prices compare to each other/analyze stock’s volatility) Example: Ratios of Closes=week 1 closing price/week 2 closing price Compute Max, Min, Average & Range of the Ratios of Closes

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How can histograms help us price a stock option? In the Excel file Option Data.xls, which contains the historical records of Walt Disney weekly closing prices, we computed 417 ratios of weekly adjusted closing prices. This set of ratios contains the information that will allow us to price an option. As a first step, we will use the computer tools of this section to analyze the ratios. Histograms, Focus on the project Probability, Mathematics, Tests, Homework, Computers Stock Option Pricing (material continues) Option Data.xls IT C Class Project

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on the project Probability, Mathematics, Tests, Homework, Computers Stock Option Pricing In the sheet Histogram of the Excel file Option Focus.xls we have used the MIN, MAX and AVERAGE functions to find that the smallest ratio is 0.7578, the largest is 1.1774, and the average of the 417 ratios is 1.0049. This shows a range of 1.1774 0.7578 = 0.4196. It is important to understand the meaning of the ratios. The number 1.0019 shows that, on average, the value of a share of Walt Disney stock rose by 0.19% per week during the last 8 years. Open the sheet Histogram to see how the following plot was constructed. Histograms, Focus (material continues) Option Focus.xls Click here for information on downloading stock data and on adjusted prices. IT C Class Project

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on the project Probability, Mathematics, Tests, Homework, Computers Stock Option Pricing Histograms, Focus Option Focus.xls (material continues) IT C Class Project

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