Solved: The Following Table Gives The Frequency Distribution Of The Daily Commuting Times (in Minutes) From Home To Work For A Sample Of 25 Employees Of A Company. Daily Commuting Time (mins) Number O

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The following table gives the frequency distribution of the daily commuting times (in minutes) from home to work for a sample of 25 employees of a company.

 Daily Commuting Time (mins) Number of Employees f Relative Frequency Cumulative Frequency Midpoint x xf (x - x?)2 0 to less than 10 4 4/25 4 5 20 268.96 10 to less than 20 9 9/25 13 15 135 40.96 20 to less than 30 6 6/25 19 25 150 12.96 30 to less than 40 4 4/25 23 35 140 184.96 40 to less than 50 2 2/25 25 45 90 556.96 25 535 1064.80
1. Construct a relative frequency distribution table for this data.

Relative frequency = frequency divided by total cumulative frequency

?f = 4+9+6+4+2=25

Calculating ?f: 4+9=13, 13+6=19, 19+4=23, 23+2=25

1. What proportion of employees has daily commute time less than 30 minutes?

4+9+6=19

1. Calculate the median daily commute time of employees. n = 5, 5/2 = 2.5, (?f)? = 4, L? = 10, C = 20 – 10 = 10, ƒ median = 9

The median class is 10 to less than 20

Me = 10 + (2.5-49)10 = 10 + (-1.5/9) 10 = 10 + (-1/6) 10 = 10 + -1 2/3 = 8 1/3

1. Calculate the median daily commute time of employees. n= 5, 5/2 = 2.5, (?f)? = 4, L? = 10, C = 20 – 10 = 10, ƒ median = 9

The median class is 10 to less than 20

Me = 10 + (2.5-4/9) 10 = 10 + (-1.5/9) 10 = 10 + (-1/6) 10 = 10 + -1 2/3 = 8 1/3

1. Calculate the mean daily commute time of employees.

First calculate the midpoint: (0+10)/2=5, (10+20)/2=15, (20+30)/2=25, (30+40)/2=35, (40+50)/2=45

Then the sum of xf: 4*5=20, 9*15=135, 6*25=150, 4*35=140, 2*45=90

Therefore, 20+135+150+140+90=535

Mean = 535/25=21.4

1. Calculate the variance for the daily commute time of employees.

Sample Variance = ?(x-x?n-1

x? = 21.4

5-21.4= (-16.4)² = 268.96; 15-21.4= (-6.4)² = 40.96; 25-21.4= (3.6)² = 12.96;

35-21.4= (13.6)² = 184.96; 45-21.4= (23.6)² = 556.96

? ?(x - x?)2 = 286.96+40.96+12.96+184.96+556.96 = 1064.80

n =5; 5-1=4

? 1064.80/4 = 266.20

n 2 Me L C wmedian n 2 Me L C wmedian