 Hi and welcome to the session. Let us just ask the following question. The question says, the distance in kilometers 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 group frequency distribution table with class size 5 for the data given above taking the first interval as 0 to 5. 5 not included. What main features do you observe from this tabular representation? Let's now look at the solution. Frequency distribution table is the method by which we can represent raw data in the form from which one can easily understand the information contained in the raw data. Frequency distribution table, we make three columns. One for the variable under study. Now here the variable under study is distance, one for the tally marks and one for the frequency. The maximum value of the distance, maximum value of distance is 32. And in the question we are given that we have to take the first interval as 0 to 5 in which 5 is not included. And we know that class intervals are of the same size. So we take the class intervals as 0 to 5, 5 to 10, 10 to 15 to 20, 20 to 25, 25 to 30, 30 to 35. In the class interval 0 to 5, 5 is not included. It will be included in the next interval. Similarly in this interval 10 will not be included. It will be included in the next interval. Now look at the data. Distance of residence of first engineer from his work places 5 kilometers. So now we will put one tally mark against the interval 5 to 10. Now again look at the data. Distance of residence of second engineer from his work places 3 kilometers. Now 3 kilometers is included in the interval 0 to 5. So we will now put one tally mark against the interval 0 to 5. Now the third distance is 10. It is included in the class interval 10 to 15. So we will now put one tally mark against this interval. Fourth distance is 20. It is covered in this interval. So we will put one tally mark against it. Sixth distance is 11. 11 is covered in this interval. So we will put one tally mark against it. Seven distance is 30. This is covered in this interval. Eighth distance is 7. But in the seventh interval, so we will put a tally mark against it. Now the distance is 12. 12 is covered in the interval 10 to 15. So we will put a tally mark against it. 31. It is covered in this interval. So we will put a tally mark against it. 19. 19 is covered in the interval 15 to 20. So put a tally mark here. 10. Covered in this interval. Now remember that we record tally marks in bunches of five. So we can write the fifth tally mark by crossing diagonally the other four tally marks. 12. It is covered in this interval. So we will put a tally mark here. 17. 17 is covered in this interval. So put a tally mark here. Or in the same pattern, we have written all the tally marks for the given intervals. Now count the tally marks in each row and write the number in the column headed by frequency. In the first row of tally marks are 5. In second row, number of tally marks are 11. Number of tally marks are 11. In fourth row, number of tally marks are number of tally marks is 1. And in seventh row, number of tally marks are 7. Quincy is, so we get that 5. Ingenious left within 0 to 5 kilometers. 11. Ingenious left within 5 to 10 kilometers. Again 11. Ingenious left within 10 to 15 kilometers. 9. Ingenious left within 15 to 20 kilometers. 1. Ingenious left within 20 to 25 kilometers. 1. Ingenious left within 25 to 30 kilometers. 2. Ingenious left within 30 to 35 kilometers. We can conclude from here that most of the Ingenious left within 5 to 10 or 10 to 15 kilometers. And very few left within 20 to 35 kilometers. So this completes the session. I hope you understood the question. Bye and take care.