 Hi and welcome to the session. I'm Shashi and I'm going to help you with the following question. Question says, 30 women were examined in a hospital by a doctor and the number of heart beats per minute were recorded and summarized as follows. Find the mean heart beats per minute for these women choosing a suitable method. This table shows recorded number of heart beats per minute for 30 women. First of all, let us understand that according to step deviation method, mean is equal to a plus h multiplied by summation fi ui upon summation fi. Now in this formula, x bar is mean, a is assumed mean, h is class size, u is xi minus a upon h. That is class mark or we can say midpoint of the interval minus assumed mean upon class size and fi is frequency. Now this formula is the key idea to solve the given question. Let us now start with the solution. First of all, we will rewrite the data given in the question. We are given number of heart beats per minute and number of women. Now we know number of women represents frequency, so we will denote it by fi. Now let us find out midpoint of every class interval. So it is represented by xi. Now midpoint of this interval is equal to 68 plus 65 upon 2 that is 66.5. Similarly midpoint of this interval or we can say class mark of this interval is equal to 71 plus 68 upon 2 that is 69.5. We know class mark is equal to upper class limit plus lower class limit upon 2. Now we will find out class mark for this interval that is 72.5. Similarly for this interval it is equal to 75.5. For this interval class mark is 78.5 and it is equal to 81.5 and 84.5 for next two intervals. Now we will choose one among the xi's as our assumed mean. So let it be 66.5. So we can write assumed mean that is a is equal to 66.5. We represent assumed mean by a. Now we will find out deviation of assumed mean from class mark of the interval. So we will find out di which is equal to xi minus a. Now here the value of xi is 66.5 and value of a is also 66.5. So di is equal to 66.5 minus 66.5 that is 0. Similarly here xi is equal to 69.5 and a is equal to 66.5. We know assumed mean is equal to 66.5. Now we will find out di that is xi minus a. So we get 69.5 minus 66.5 is equal to 3. So we will write 3 here. Now we know xi is equal to 72.5 and assumed mean is 66.5. So deviation of assumed mean from 72.5 is 6. 72.5 minus 66.5 is equal to 6. Similarly deviation of assumed mean from 75.5 is equal to 9. 75.5 minus 66.5 is equal to 9. Similarly 78.5 minus 66.5 is equal to 12. So deviation of assumed mean from 78.5 is 12. Similarly 81.5 minus 66.5 is equal to 15. So here deviation is equal to 15 and 84.5 minus 66.5 is equal to 18. So deviation is equal to 18 in this case. Now clearly we can see all these values are divisible by 3 and 3 is the class size. So we will divide deviation that is di by class size and h denotes class size. Now we know class size that is h is equal to 3. Now dividing 0 by 3 we get 0. 3 divided by 3 is equal to 1. 6 divided by 3 is equal to 2. 9 divided by 3 is equal to 3. 12 divided by 3 is equal to 4. 15 divided by 3 is equal to 5. And 18 divided by 3 is equal to 6. Let us assume that di upon h is equal to ui. Now we will find the product fi ui. Now 2 multiplied by 0 is equal to 0. 4 multiplied by 1 is equal to 4. 3 multiplied by 2 is equal to 6. 8 multiplied by 3 is equal to 24. 7 multiplied by 4 is equal to 28. 4 multiplied by 5 is equal to 20. 2 multiplied by 6 is equal to 12. Now we will find out summation fi. It is equal to sum of all these frequencies. We know total number of women is equal to 30. And now we will find out summation fi ui. It is equal to sum of all these products. So it is equal to 94. From key idea we know mean is equal to assumed mean that is a plus h multiplied by summation fi ui upon summation fi. Now substituting corresponding values of summation fi ui, summation fi h and a in this formula we get mean is equal to 66.5 plus 3 multiplied by 94 upon 30. Now multiplying these 2 terms we get 9.4. So mean is equal to 66.5 plus 9.4. Now adding these 2 terms we get mean is equal to 75.9. So we get the mean heart beats per minute is equal to 75.9. So this is our required answer. This completes the session. Hope you understood the solution. Take care and have a nice day.