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प्रश्न
The value of π up to50 decimal places is given below:-
3.14159265358979323846264338327950288419716939937510
(i) Make a frequency distribution of the digits from 0 to 9 after the decimal point.
(ii) What are the most and the least frequently occurring digits?
उत्तर
(i) By observation of the digits after decimal point, the required table can be constructed as follows.
| Digit | Frequency |
| 0 | 2 |
| 1 | 5 |
| 2 | 5 |
| 3 | 8 |
| 4 | 4 |
| 5 | 5 |
| 6 | 4 |
| 7 | 4 |
| 8 | 5 |
| 9 | 8 |
| Total | 50 |
(ii) It can be observed from the above table that the least frequency is 2 of digit 0, and the maximum frequency is 8 of digit 3 and 9. Therefore, the most frequently occurring digits are 3 and 9 and the least frequently occurring digit is 0.
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संबंधित प्रश्न
The distance (in km) of 40 engineers from their residence to their place of work were found as follows:-
| 5 | 3 | 10 | 20 | 25 | 11 | 13 | 7 | 12 | 31 |
| 19 | 10 | 12 | 17 | 18 | 11 | 32 | 17 | 16 | 2 |
| 7 | 9 | 7 | 8 | 3 | 5 | 12 | 15 | 18 | 3 |
| 12 | 14 | 2 | 9 | 6 | 15 | 15 | 7 | 6 | 12 |
Construct a grouped frequency distribution table with class size 5 for the data given above taking the first interval as 0-5 (5 not included). What main features do you observe from this tabular representation?
Thirty children were asked about the number of hours they watched TV programmes in the previous week. The results were found as follows:-
| 1 | 6 | 2 | 3 | 5 | 12 | 5 | 8 | 4 | 8 |
| 10 | 3 | 4 | 12 | 2 | 8 | 15 | 1 | 17 | 6 |
| 3 | 2 | 8 | 5 | 9 | 6 | 8 | 7 | 14 | 12 |
(i) Make a grouped frequency distribution table for this data, taking class width 5 and one of the class intervals as 5 - 10.
(ii) How many children watched television for 15 or more hours a week?
Write the class size and class limits in each of the following:
(i) 104, 114, 124, 134, 144, 154, and 164
(ii) 47, 52, 57, 62, 67, 72, 77, 82, 87, 92, 97 and 102
(iii) 12.5, 17.5, 22.5, 27.5, 32.5, 37.5, 42.5, 47.5
Construct a frequency table with equal class intervals from the following data on the monthly
wages (in rupees) of 28 laborers working in a factory, taking one of the class intervals as
210-230 (230 not included):
220, 268, 258, 242, 210, 268, 272, 242, 311, 290, 300, 320, 319, 304, 302, 318, 306, 292,
254, 278, 210, 240, 280, 316, 306, 215, 256, 236.
The daily maximum temperatures (in degree celsius) recorded in a certain city during the
month of November are as follows:
25.8, 24.5, 25.6, 20.7, 21.8, 20.5, 20.6, 20.9, 22.3, 22.7, 23.1, 22.8, 22.9, 21.7, 21.3, 20.5,
20.9, 23.1, 22.4, 21.5, 22.7, 22.8, 22.0, 23.9, 24.7, 22.8, 23.8, 24.6, 23.9, 21.1
Represent them as a frequency distribution table with class size 1°C.
The daily minimum temperatures in degrees Ce1siu& recorded in a certain Arctic region are
as follows:
−12.5, −10.8, −18.6, −8.4, −10.8, −4.2, −4.8, −6.7, −13.2, −11.8, −2.3, 1.2, 2.6, 0, 2.4,
0, 3.2, 2.7, 3.4, 0, − 2.4, − 2.4, 0, 3.2, 2.7, 3.4, 0, − 2.4, − 5.8, -8.9, 14.6, 12.3, 11.5, 7.8,2.9.
Represent them as frequency distribution table taking − 19.9 to − 15 as the first class
interval.
Given below is a cumulative frequency distribution table showing the ages of people living in a locality:
| Ace in years | No. of persons |
| Above 108 | 0 |
| Above 96 | 1 |
| Above 84 | 3 |
| Above 72 | 5 |
| Above 60 | 20 |
| Above 48 | 158 |
| Above 36 | 427 |
| Above 24 | 809 |
| Above 12 | 1026 |
| Above 0 | 1124 |
Prepare a frequency distribution table
In the class intervals 10-20, 20-30, 20 is taken in
Convert the given frequency distribution into a continuous grouped frequency distribution:
| Class interval | Frequency |
| 150 – 153 | 7 |
| 154 – 157 | 7 |
| 158 – 161 | 15 |
| 162 – 165 | 10 |
| 166 – 169 | 5 |
| 170 – 173 | 6 |
In which intervals would 153.5 and 157.5 be included?
The following are the marks (out of 100) of 60 students in mathematics.
16, 13, 5, 80, 86, 7, 51, 48, 24, 56, 70, 19, 61, 17, 16, 36, 34, 42, 34, 35, 72, 55, 75, 31, 52, 28, 72, 97, 74, 45, 62, 68, 86, 35, 85, 36, 81, 75, 55, 26, 95, 31, 7, 78, 92, 62, 52, 56, 15, 63, 25, 36, 54, 44, 47, 27, 72, 17, 4, 30.
Construct a grouped frequency distribution table with width 10 of each class, in such a way that one of the classes is 10 – 20 (20 not included).
