Question

6. The starting annual salaries for a sample of 35 liberal arts graduates Note: you could answer this question using excel or by hand. Your choice Starting Salary ($thousands) Relative Frequency Frequency 0.086 0.086 0.143 0.257 0.257 0.114 0.029 0.029 25 - (26) 26 - (27) 27 - (28) 28 - (29) 29 - (30) 30 - (31) 31 - (32) 32 - (33) 4 Construct the cumulative frequency distribution b.Construct the cumulative relative frequency distribution Plot the ogive Using your plot in part (c), find an approximate value for the median starting annual salary for liberal-arts graduates d.

Answer 1

GIVEN:

The frequency distribution table:

Starting salary	Frequency	Relative Frequency
25-26	3	0.086
26-27	3	0.086
27-28	5	0.143
28-29	9	0.257
29-30	9	0.257
30-31	4	0.114
31-32	1	0.029
32-33	1	0.029

(a) CUMULATIVE FREQUENCY DISTRIBUTION:

The cumulative frequency is calculated by adding each frequency from a frequency distribution table to the sum of its predecessors.

Starting salary	Frequency	Cumulative Frequency	Relative Frequency
25-26	3	3	0.086
26-27	3	3+3=6	0.086
27-28	5	6+5=11	0.143
28-29	9	11+9=20	0.257
29-30	9	20+9=29	0.257
30-31	4	29+4=33	0.114
31-32	1	33+1=34	0.029
32-33	1	34+1=35	0.029

(b) CUMULATIVE RELATIVE FREQUENCY DISTRIBUTION:

The cumulative frequency is calculated by adding each relative frequency from a frequency distribution table to the sum of its predecessors.

Starting salary	Frequency	Cumulative Frequency	Relative Frequency	Cumulative Relative Frequency
25-26	3	3	0.086	0.086
26-27	3	3+3=6	0.086	0.086+0.086=0.172
27-28	5	6+5=11	0.143	0.172+0.143=0.315
28-29	9	11+9=20	0.257	0.315+0.257=0.572
29-30	9	20+9=29	0.257	0.572+0.257=0.829
30-31	4	29+4=33	0.114	0.829+0.114=0.943
31-32	1	33+1=34	0.029	0.943+0.029=0.972
32-33	1	34+1=35	0.029	0.972+0.029=1

(c) OGIVE CURVE:

An ogive graph plots cumulative frequency on the y-axis and class boundaries along the x-axis. Each point should be plotted on the upper limit of the class boundary.

For example, if your first class boundary is 0 to 10, the point should be plotted at 10. Connect the dots with straight lines. the ogive is one continuous line, made up of several smaller lines that connect pairs of dots, moving from left to right.

Upper class boundary of Starting salary	Cumulative Frequency
26	3
27	6
28	11
29	20
30	29
31	33
32	34
33	35

An ogive curve for the above table is given below:

OsIVE CURVE 40 R5 15 to 5 25 27 28 29 31 32 3334 Uper dlast Bsurday

(d) APPROXIMATE VALUE OF MEDIAN FROM OGIVE CURVE:

• Let N be the total observations of sample data given. N will also be the cumulative frequency of the last interval which is
  35
  . Find the
  (N/2)
  th item and mark it on the y-axis.
• In the given problem the
  (N/2)
  th item is
  35/2= 17.5
  
• Draw a perpendicular from 17.5 from y axis to the right to cut the Ogive curve at point A. From point A where the Ogive curve is cut, draw a perpendicular on the x-axis.
• The point at which it touches the x-axis will be the median value of the series as shown in the graph.

OGIVE CURVE 35 25 15 to e Median=28.5 Approximale Medion 285 5 3i za 33 34 25 27 28 29 γο Upper class Bourdah

Thus the approximate value of median starting annual salary is
28.5
($thousands).