- The following numbers give the weights of 55 students of a class. Prepare a suitable frequency table: 42, 74, 40, 60, 82, 115, 41, 61, 75, 83, 63, 53, 110, 76, 84, 50, 67, 65, 78, 77, 56, 95, 68, 69, 104, 80, 79, 79, 54, 73, 59, 81, 100, 66, 49, 77, 90, 84, 76, 42, 64, 69, 70, 80, 72, 50, 79, 52, 103, 96, 51, 86, 78, 94, 71.
(a) Draw the histogram and frequency polygon of the above data.
(b) For the above heights, prepare a cumulative frequency table and draw the less than ogive.
Sol: Given the weights of 55 students, we can prepare a frequency table by categorizing the data into class intervals. Let's use intervals of size 10 to create the frequency table.
- Firstly, find the minimum and maximum weight to determine the range. MIN = 40, MAX = 115.
- Let's choose class intervals of size 10: 40-49, 50-59, 60-69, etc.
- Count the number of students in each interval.
(a) Frequency polygon:
(b) Cumulative frequency table:
Interval |
Cumulative
Frequency |
40-49 |
7 |
50-59 |
14 |
60-69 |
24 |
70-79 |
40 |
80-89 |
47 |
90-99 |
51 |
100-109 |
54 |
110-119 |
55 |
(b) Ogive curve:
2. What are the points to be borne in mind in the formation of a frequency table?
Choosing appropriate class intervals, from a frequency table for the following data: 10.2, 0.5, 5.2, 6.1, 3.1, 6.7, 8.9, 5.4, 3.6, 9.2, 6.1, 7.3, 2.0, 1.3, 6.4, 8.0, 4.3, 4.7, 12.4, 8.6, 13.1, 3.2, 9.5, 7.6, 4.0, 5.1, 8.1, 1.1, 11.5, 3.1, 6.8, 7.0, 8.2, 2.0, 3.1, 6.5, 11.2, 12.0, 5.1, 10.9, 11.2, 8.5, 2.3, 3.4, 5.2, 10.7, 4.9, 6.2.
- Understand the purpose: The table should be suitable for the objective of the analysis. For instance, detailed classifications may be required for an in-depth study, while broader categories may suffice for an overview.
- Minimum and Maximum values: Determine the range of the data by identifying the minimum and maximum values. This helps in defining the classes.
- Class Intervals: It should be uniform, meaning that they should have equal width, unless the data necessitates variable width due to its nature. Choose a suitable class width based on the range and the number of observations. The width should neither be too small nor too large. The starting point of the first-class intervals is often a convenient number slightly less than or equal to the smallest observation.
- The number of classes typically ranges from 5 to 20. The formula 2 power k > n, where n is the number of observations and k is the number of classes, can be a good starting point.
- The class intervals should be distinct and not overlap.
- If there are exceptionally high or low values, consider using open-ended classes like "more than or less than".
- Determine the class mid points, boundaries, and limits. This helps in plotting graphs and further analysis.
- They can be used for raw data to count the frequency for each class.
- If required, include a column for cumulative frequency.
Interval |
Frequency |
0.5 - 3.0 |
6 |
3.0 - 5.5 |
15 |
5.5
- 8.0 |
10 |
8.0
- 10.5 |
9 |
10.5
- 13.0 |
7 |
Row |
Age |
Frequency |
Percentage |
1 |
Below 25 |
243 |
68.0672268907563 |
2 |
25 - 35 |
55 |
15.406162464 |
3 |
35 – 45 |
34 |
9.5238095238095237 |
4 |
Above 45 |
25 |
7.0028011204481793 |
Row |
Occupation |
Frequency |
Percentage |
1 |
Student |
203 |
56.862745098039213 |
2 |
Government Employee |
27 |
7.56302521008 |
3 |
Private Employee |
91 |
25.490196078431371 |
4 |
Self-employee |
24 |
6.7226890756302522 |
5 |
Un-employee |
12 |
3.3613445378151261 |
Row |
Global warming |
Frequency |
Percentage |
1 |
Strongly Agree |
135 |
37.815126050420169 |
2 |
Agree |
182 |
50.980392156862742 |
3 |
Disagree |
28 |
7.8431372549019605 |
4 |
Strongly Disagree |
12 |
3.361344537 |
Row |
Knowledge about
Ev |
Frequency |
Percentage |
1 |
Newspapers |
46 |
12.88515406162465 |
2 |
Magazine |
57 |
15.96638655 |
3 |
Television |
55 |
15.406162464985995 |
4 |
Internet |
199 |
55.742296918767508 |
Row |
Charging Points |
Frequency |
Percentage |
1 |
Each 50 KM |
129 |
36.134453781512605 |
2 |
Each 100 KM |
141 |
39.495798319327733 |
3 |
Each 150 KM |
54 |
15.12605042 |
4 |
Each 200 KM |
33 |
9.2436974789915958 |
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