Statistics: Histogram and Frequency Percentage Frequency Essay

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Name: Anh Pham ID: 12572821 Section 003 #1. a) A random sample of 30 customer records for a physician's office show the days to collect insurance payment. Step 1: List the possible values: The possible values for the discrete variables are 20 through 79. Step 2: Determine the width of the data by computing the range In this question, k is 6. Step 3:Define the class size We have: Class width=Range/Number of classes=(79-­‐20)/6=9.8 or 10 20-­‐30 31-­‐40 41-­‐50 51-­‐60 61-­‐70 71-­‐80 Step 4: Count the number of occurances at each value. Classes Frequency 20-­‐30 4 31-­‐40 13 41-­‐50 6 51-­‐60 4 61-­‐70 2 71-­‐80 1 Total 30 b) Find the relative frequency and percentage frequency Classes Relative frequency Percentage frequency (f/n) 20-­‐30 0.13 13.33% 31-­‐40 0.43 43.33% 41-­‐50 0.2 20.00% 51-­‐60 0.13 13.33% 61-­‐70 0.06 6.66% 71-­‐80 0.03 3.33% 1 100.00% c) We have: a (number of days) >= 56 is considered uncollectible Therefore, there are 6 customers (60; 66; 65; 79; 56; 56) whose payment are considered as uncollectible We have: Fraction of 30 accounts which should be turned over to the collection agency is: 6/30=0.2 or 20% d) Draw the frequency histogram and the frequency polygon

Classes 20-­‐30 31-­‐40 41-­‐50 51-­‐60 61-­‐70 71-­‐80

Frequency 4 13 6 4 2 1 30

Relative frequency (f/n) frequency Percentage 0.13 0.43 0.2 0.13 0.06 0.03 1

13.33% 43.33% 20.00% 13.33% 6.66% 3.33% 100.00%

Cu. relative 4/30 17/30 23/30 27/30 29/30 30/30 30/30

Frequency Histogram

14 12 Frequency 10 8 6 4 2 0 20-­‐30 31-­‐40 41-­‐50 51-­‐60 61-­‐70 71-­‐80 Days of collecAng Frequency

Frequency Polygon 14 12 10 8 6 4 2 0 20-­‐30 31-­‐40 41-­‐50 51-­‐60 61-­‐70 71-­‐80 Frequency

e) The distribution of the data is skewed to the right or (+) skewed. f) The modal class is the class with highest frequency. Therefore, modal class is customers whose days of payment from 31 to 40 days.

Exercise 2.28 page 64 North America 2007 Column1 Types Barrels per day Percentage 1 Kerosene 1,685 2 Asphalt, LPG 9,384 3 Residuals 15,422 4 Diesel&home heating 91,344 5 Gasoline 298,833

0.40% 2.25% 3.70% 21.92% 71.72%

North America sales product per day 0.004 0.0225 0.037 Kerosene 0.2192 0.7172 Asphalt, LPG

Residuals

Diesel&home heaeng Gasoline

b) Column1 1 2 3 4 5

United Kingdom 2007 Types Barrels per day Percentage Residuals 3,728 Kerosene 4,020 Asphalt, LPG 4,213 Gasoline 14,356 Diesels&home heating 14,785

9.07% 9.78% 10.25% 34.93% 35.97%

United Kingdom sales product per day 0.0907 0.3597 0.0978 Kerosene 0.1025 Asphalt, LPG 0.3493 Gasoline Residuals

c) Construct a bar chart that effectively compare the daily product sales for North America and United Kingdom.

Asphalt, LPG and other
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