Frequency Distribution

Frequency distribution:

The table below contains data collected:

DATE

MINUTES TO DRIVE TO WORK

MON/5 OCT

30 MIN

TUES/6 OCT

30 MIN

WED/7 OCT

1/12

Frequency Distribution

20 MIN

THURS/8 OCT

20 MIN

FRI/9 OCT

SICK LEAVE/DID NOT GO TO WORK

MON/12 OCT

COLUMBUS DAY/DID NOT GO TO WORK

TUES/13 OCT

SICK LEAVE/DID NOT GO TO WORK

WED/14 OCT

SICK LEAVE/DID NOT GO TO WORK

2/12

Frequency Distribution

THURS/15 OCT

SICK LEAVE/DID NOT GO TO WORK

FRI/16 OCT

SICK LEAVE/DID NOT GO TO WORK

We assume that for the days that the individual did not report to work the minutes taken to drive to work amount to zero, therefore the table is summarized as follows:

DATE

MINUTES TO DRIVE TO WORK

MON/5 OCT

30 MIN

3/12

Frequency Distribution

TUES/6 OCT

30 MIN

WED/7 OCT

20 MIN

THURS/8 OCT

20 MIN

FRI/9 OCT

0

MON/12 OCT

0

4/12

Frequency Distribution

TUES/13 OCT

0

WED/14 OCT

0

THURS/15 OCT

0

FRI/16 OCT

0

The frequency distribution table will contain three classes and they include the class 0 to 10, 11 to 21 and 22 to 32, the table below summarizes the frequencies:

5/12

Frequency Distribution

class

frequency

0 to 10

6

11 to 21

2

22 to 32

2

total

10

6/12

Frequency Distribution

Standard deviation:

The standard deviation for grouped data is calculated as follows:

Sd = [(FX2/ f) – (FX/F)2]½

The table below summarizes the midpoints of the classes and calculations made to determine the standard deviation:

x

class

Frequency(FX)

7/12

Frequency Distribution

mid point

FX

FX2

0 to 10

6

5

30

900

11 to 21

2

16

8/12

Frequency Distribution

32

1024

22 to 32

2

27

54

2916

total

10

116

9/12

Frequency Distribution

4840

Given

Sd = [(FX2/ f) – (FX/F)2]½

Then

Sd = [(4840/ 10) – (116/10)2]½

Sd = 18.69331

Normal distribution:

The central limit theorem givens the conditions and properties of a normal distribution, they include:

68% of data is contained within one standard deviation, 95% of the data is contained within two standard deviations, the mean value is determined as follows:

Mean = FX/F

10/12

Frequency Distribution

Mean = 116/ 10 = 11.6

68% of observations:

Standard deviation = 18.69331

Mean = 11.6

Range of data

(11.6+ 18.69331) and (1.6 – 18.69331)

(30.29331) and (-7.09331)

From our case data that ranged from -7.09331 to 30.29331 is greater than 68%, therefore the distribution is not a normal distribution.

Implications:

Given that this is not a normal distribution this means that statistical tests that assume normal

11/12

Frequency Distribution

distribution cannot be applied, also this means that the sample is not large enough given that the central limit theorem states that as the number of random numbers increase the data assumes a normal distribution.

## REFERENCE:

Mendenhall, W. (2003) Introduction to statistics, Prentice Hall press, New  Jersey

12/12