The following table gives the cumulative frequency distribution of the commuting

Question

The following table gives the cumulative frequency distribution of the commuting time (in minutes) from home to work for a sample of 400 persons selected from a city. Time (minutes) f 0 to less than 10 63 0 to less than 20 158 0 to less than 30 228 0 to less than 40 293 0 to less than 50 348 0 to less than 60 400 The sample size is: The percentage of persons who commute for less than 30 minutes, rounded to two decimal places, is: % The cumulative relative frequency of the fourth class, rounded to four decimal places, is: The percentage of persons who commute for 40 or more minutes, rounded to two decimal places, is: % The percentage of persons who commute for less than 50 minutes, rounded to two decimal places, is: % The number of persons who commute for 20 or more minutes is:

Explanation / Answer

The cumulative frequency distribution table is:

Sample size = 400

% of persons who commute less than 30 minutes = 228 / 400 = 57%

Cumulative relative frequency of fourth class = 293 / 400 = 0.7325

% of persons who commute for 40 or more minutes

= 100% - % who commutes less than 40 minutes

= 100% - (293 / 400) * 100

= 100% - 73.25%

= 26.75%

% of persons who commute less than 50 minutes = 348 / 400 = 87%

Number of persons who commute for 20 or more minutes = 400 - 158 = 242

x F(x) 0 to less than 10 63 0 to less than 20 158 0 to less than 30 228 0 to less than 40 293 0 to less than 50 348 0 to less than 60 400

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