Histogram, cummulative frequency curve

Histogram consists of rectangular bar placed side by side. The vertical axis represents the frequency while the horizontal axis represents the variable being represented. The histogram has no gaps between the bars.

In drawing the histogram for a grouped data, the class boundary is written on the horizontal axis. the centre of the base of each rectangular bar corresponds to the class mark of the variable.

Frequency Polygon:This is a line graph of a frequency distribution. The graph is obtained by joining the mid-points(class marks) of the top of the histogram by line segments.

Frequency Curve: It is a smooth curve that joins the middle of the tops of the histogram.

Example: 4

Draw a histogram and a frequency polygon for the frequency distribution below:

Class interval	1 – 5	6 – 10	11 – 15	16 – 20	21 – 25
Frequency	3	5	7	6	4

Solution:

Exercise

The table shows the mark scored by some student in an examination

Mark	0-9	10 – 19	20 – 29	30 – 39	40 – 49	50 – 59	60 – 69	70 – 79	80 – 89	90 – 99
Frequency	7	11	12	20	29	34	30	25	21	6

1. a) Construct a cummulative frequency table for the distribution and draw a cummulative frequency curve.
2. b) Use the curve to estimate, correct to one decimal place, the lowest one for distinction if 50% of the students passed with the distinction.

                                                            Solution

Mark%	Frequency	Class mark (x)	Cum. freq.	Upper class boundary
0 – 9	7	4.5	7	9.5
10 – 19	11	14.5	18	19.5
20 – 29	17	25.5	35	29.5
30 – 39	20	35.5	55	39.5
40 – 49	29	45.5	84	49.5
50 – 59	34	55.5	118	59.5
60 – 69	30	65.5	148	69.5
70 – 79	25	75.5	173	79.5
80 – 89	21	85.5	194	89.5
90 – 99	6	95.5	200	99.5

1. c) Use the cum. freq. curve to find the
2. Median ii. Lower quartile

Median = 200 = 1ooth class = 54.5%

2

Lower quartile =   n = 200 50th Class

4       4

=35.5%

Cummulative Frequency

1. b) 5%

5 10; 200 – 10 = 190

100

from the graph

the lowest mark with distinction is 87.5%