Mathematics
The number of matchsticks in 40 boxes on counting was found as given below:
44, 41, 42, 43, 47, 50, 51, 49, 43, 42, 40, 42, 44, 45, 49, 42, 46, 49, 45, 49, 45, 47, 48, 43, 43, 44, 48, 43, 46, 50, 43, 52, 46, 49, 52, 51, 47, 43, 43, 45.
Taking classes 40 - 42, 42 - 44 ……, construct the frequency distribution table for the above data. Also draw a combined histogram and frequency polygon to represent the distribution.
Answer
First represent the given data in a frequency distribution table as shown below:
| Class Intervals | Class marks | Tally Marks | Frequency |
|---|---|---|---|
| 40 - 42 | 41 | II | 2 |
| 42 - 44 | 43 | 12 | |
| 44 - 46 | 45 | 7 | |
| 46 - 48 | 47 | 6 | |
| 48 - 50 | 49 | 7 | |
| 50 - 52 | 51 | IIII | 4 |
| 52 - 54 | 53 | II | 2 |
Steps of construction of histogram :
Since, the scale on x-axis starts at 38, a kink is shown near the origin on x-axis to indicate that the graph is drawn to scale beginning at 38.
Take 1 cm along x-axis = 2 units.
Take 1 cm along y-axis = 2 units.
Construct rectangles corresponding to the above continuous frequency distribution table.
The required histogram is shown in the adjoining figure.
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 the first end point with the mid-point of class 38 - 40 with zero frequency, and join the other end point with the mid-point of class 54 - 56 with zero frequency.
The required frequency polygon is shown by thick line segments in the diagram.
Related Questions
In a study of diabetic patients, the following data was obtained :
Age (in years) No. of patients 10 - 20 3 20 - 30 8 30 - 40 30 40 - 50 36 50 - 60 27 60 - 70 15 70 - 80 6 Represent the above data by a histogram and a frequency polygon.
The water bills (in rupees) of 32 houses in a locality are given below:
30, 48, 52, 78, 103, 85, 37, 94, 72, 73, 66, 52, 92, 65, 78, 81, 64, 60, 75, 78, 108, 63, 71, 54, 59, 75, 100, 103, 35, 89, 95, 73.
Taking class intervals 30 - 40, 40 - 50, 50 - 60, ……, form frequency distribution table.
Construct a combined histogram and frequency polygon.
The runs scored by two teams A and B on the first 42 balls in a cricket match are given below :
No. of balls Runs scored by Team A Runs scored by Team B 1 - 6 2 5 7 - 12 1 6 13 - 18 8 2 19 - 24 9 10 25 - 30 4 5 31 - 36 5 6 37 - 42 6 3 The histogram showing the weekly wages (in rupees) of workers in a factory is given alongside.
Answer the following about the frequency distribution:
(i) What is the frequency of the class 400 - 425?
(ii) What is the class having minimum frequency?
(iii) What is the cumulative frequency of the class 425 – 450?
(iv) Construct a frequency and cumulative frequency table for the given distribution.