The value of π upto 50 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?
Solution:
(i) We can represent the digits from 0 to 9 by constructing a simple, ungrouped frequency distribution table as follows.
|
DIGITS |
TALLY MARKS |
FREQUENCY OF OCCURRENCE |
|
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 easily observed from the table that
- The most frequently occurring digits are 3 and 9, with a max frequency of 8.
- The least frequently occurring digit is ‘0’ with the lowest frequency of 2.
☛ Check: NCERT Solutions Class 9 Maths Chapter 14
Video Solution:
The value of π up to 50 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?
NCERT Solutions for Class 9 Maths Chapter 14 Exercise 14.2 Question 7
It is given that value of π up to 50 decimal places as 3.14159265358979323846264338327950288419716939937510. We have prepared an ungrouped frequency distribution table as given in the solution and found that the most frequently occurring digits are 3 and 9, with a max frequency of 8 and the least frequently occurring digit is ‘0’ with the lowest frequency of 2.
☛ Related Questions:
- The distance (in km) of 40 engineers from their residence to their place of work was 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 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?
- The relative humidity (in %) of a certain city for a month of 30 days was as follows: 98.1 98.6 99.2 90.3 86.5 95.3 92.9 96.3 94.2 95.1 89.2 92.3 97.1 93.5 92.7 95.1 97.2 93.3 95.2 97.3 96.2 92.1 84.9 90.2 95.7 98.3 97.3 96.1 92.1 89 (i) Construct a grouped frequency distribution table with classes 84 - 86, 86 - 88, etc. (ii) Which month or season do you think this data is about? (iii) What is the range of this data?
- The heights of 50 students, measured to the nearest centimeters, have been found to be as follows: 161 150 154 165 168 161 154 162 150 151 162 164 171 165 158 154 156 172 160 170 153 159 161 170 162 165 166 168 165 164 154 152 153 156 158 162 160 161 173 166 161 159 162 167 168 159 158 153 154 159 i) Represent the data given above by a grouped frequency distribution table, taking the class intervals as 160-165, 165-170, etc. ii) What can you conclude about their heights from the table?
- A study was conducted to find out the concentration of sulphur dioxide in the air in parts per million (ppm) of a certain city. The data obtained for 30 days is as follows: 0.03 0.08 0.08 0.09 0.04 0.17 0.16 0.05 0.02 0.06 0.18 0.20 0.11 0.08 0.12 0.13 0.22 0.07 0.08 0.01 0.10 0.06 0.09 0.18 0.11 0.07 0.05 0.07 0.01 0.04 i) Make a grouped frequency distribution table for this data with class intervals as 0.00 - 0.04, 0.04 - 0.08 and so on. ii) For how many days, was the concentration of sulphur dioxide more than 0.11 parts per million?
visual curriculum