 Hello and welcome to the session. My name is Mansi and I am going to help you with the following question. The question says, 100 surnames were randomly picked up from a local telephone directory and a frequency distribution of the number of letters in the English alphabet in the surnames was found. So here we have a table where we have number of letters 1, 2, 4, 4, 2, 6, 6, 2, 8, 8, 2, 12 and 12 to 20. Number of surnames are 6, 30, 44, 16 and 4 respectively. Now we have to draw a histogram to depict the given information and second we have to write the class interval in which the maximum number of surnames lie. So let us see the solution to this one. Now what we notice in this table is that class size of each interval is not same. So we make another table where we have four columns. One would be the number of letters they are 1 to 4, 4 to 6, 6 to 8, 8 to 12 and 20, 12 to 20. Now the frequency is 6, 30, 44, 16, 4 that is 6, 30, 44, 16, 4. Now we find the width of each interval. Here the width of interval will be 4 minus 1 that is 3, 6 minus 4, 2, 8 minus 6, 2, 12 minus 8, 4 and 20 minus 12, 8. Now what we do is we select a class interval with the minimum class size. Here it is 2. Now the lengths of the rectangle are now modified to be proportionate to the class size 2. Now we see that when width of interval is 3 then length of rectangle is 6. So when width of interval will be 2, length of rectangle will be 6 by 3 into 2 that is equal to 4. Similarly here we will have 30 by 2 into 2 is equal to 30 only. Here also we will have 44 as it is. Here we will have 16 divided by 4 into 2 that is equal to 8 and here we have 4 divided by 8 into 2 that is equal to 1. Now with this table let us draw a histogram. So now we see that in this graph we will draw the histogram. On the x-axis we have taken the number of letters and on the y-axis we have taken number of surnames. So let us draw the histogram with this information where number of letters will be this and length of rectangle will be this. So this will be the required histogram where we see that 0 to 4 we have or 1 to 4 we have 4, 4 to 6 is 30, 6 to 8 is 44, 8 to 12 is 8 and 12 to 20 is 1. So this will be our answer to the question. I hope that you understood the question and enjoyed the session. Have a good day.