Mathematics
Draw a histogram and the frequency polygon from the following data:
| Class interval | Frequency |
|---|---|
| 20 - 25 | 30 |
| 25 - 30 | 24 |
| 30 - 35 | 52 |
| 35 - 40 | 28 |
| 40 - 45 | 46 |
| 45 - 50 | 10 |
Answer
Frequency distribution table :
| Class interval | Class marks | Frequency |
|---|---|---|
| 20 - 25 | 22.5 | 30 |
| 25 - 30 | 27.5 | 24 |
| 30 - 35 | 32.5 | 52 |
| 35 - 40 | 37.5 | 28 |
| 40 - 45 | 42.5 | 46 |
| 45 - 50 | 47.5 | 10 |
Steps of construction of histogram:
Since, the scale on x-axis starts at 15, a break (kink) is shown near the origin on x-axis to indicate that the graph is drawn to scale beginning at 15.
Take 1 cm along x-axis = 5 units.
Take 1 cm along y-axis = 10 units.
Construct rectangles corresponding to the above continuous frequency distribution table.
Steps of construction of frequency polygon:
Mark the mid-points of upper bases of rectangles of the histogram.
Join the consecutive mid-points by line-segments.
Join first end point with mid-point of class 15 - 20 with zero frequency, and join the other end point with the mid point of class 50 - 55 with zero frequency.
The required frequency polygon is shown by thick line segments in the diagram.
Related Questions
In a study of diabetic patients in a village, the following observations were noted :
Age in years No. of patients 10 - 20 2 20 - 30 5 30 - 40 12 40 - 50 19 50 - 60 9 60 - 70 4 Represent the above data by a frequency polygon.
The ages (in years) of 360 patients treated in a hospital on a particular day are given below :
Age in years No. of patients 10 - 20 90 20 - 30 40 30 - 40 60 40 - 50 20 50 - 60 120 60 - 70 30 Draw a histogram and a frequency polygon on the same graph to represent the above data.
Draw a histogram for the following data:
Class interval Frequency 600 - 640 18 640 - 680 45 680 - 720 153 720 - 760 288 760 - 800 171 800 - 840 63 Using this histogram, draw the frequency polygon on the same graph.
Draw an ogive to represent the following data:
Class interval Frequency 400 - 450 16 450 - 500 25 500 - 550 40 550 - 600 32 600 - 650 18 650 - 700 27 700 - 750 9