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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 2 Me L C wmedian

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 2 Me L C wmedian

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

Answer Preview

(a) Relative frequency = frequency divided by totalfrequency Total frequency=f = 4+9+6+4+2=25 So Respective Relative Frequencies are 4/25, 9/25, 6/25, 4/25, 2/25 (b) Proportion of employees = n

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