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# The value of $ \pi $ 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?

The value of \( \pi \) upto 50 decimal places is given.

To do:

We have to

(i) Make a frequency distribution of the digits from 0 to 9 after the decimal point.

(ii) Find the most and the least frequently occurring digits.

Solution:

(i) The frequency distribution of the digits from 0 to 9 after the decimal point is given in the table below as follows:

Digits | Frequency |

0 | 2 |

1 | 5 |

2 | 5 |

3 | 8 |

4 | 4 |

5 | 5 |

6 | 4 |

7 | 4 |

8 | 5 |

9 | 8 |

Total | 50 |

(ii) The digit having the least frequency occurs the least number of times.

Here, $0$ occurs twice.

This implies,

It has a frequency of 2.

Therefore, the least frequently occurring digit is $0$.

The digit having the highest frequency occurs most number of times.

Here, $3$ and $9$ occur eight times.

This implies,

$3$ and $9$ have a frequency of 8.

Therefore, the most frequently occurring digits are $3$ and $9$.

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