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Reproductive Phase

Table of Contents Reproductive Phase Males Females Menstrual Cycle Summary Did You Know? What’s Next? In the previous segment of […]

Mean using the Step Deviation Method – Part 1Summary: We understand what Step Deviations are. We also understand how the values in our data set are modified to generate Step Deviations.We saw this formula in the previous lesson. = +a (1)It gives us the relationship between the MEAN and the ASSUMED MEAN. And remember this data set? We use it to find the Mean.Class intervalxifi20 – 3025230 – 4035340 – 50a = 45450 – 6055360 – 70651We used the Assumed Mean method to find the Mean. As the name suggests, we ASSUMED our Mean to be 45. We know that the assumed mean method simplifies calculations to find the Mean ‘x bar’. Assumed Mean Method → Simplifies Calculations to find the MeanHow is the calculation SIMPLIFIED?To understand this, let us plot our values on a number line. We know that this is our assumed Mean.By subtracting the ASSUMED MEAN 45, from our values, we work with smaller numbers. For our data set, we subtract 45 from all our s, since we have chosen 45 as our ASSUMED MEAN.So we get a new set of numbers after subtraction. The subtraction results in the deviation of our values to the LEFT. values shifted to the left → ( – a)This diagram shows our before and after the Deviation by ‘a’ units. You can say that this number line gets shifted to the left by 45 units. So we add another column to our table. It is a column for ‘ minus a’. So from this table, we are able to see the values before and after they are SHIFTED.Class intervalxifi (xi -a)20 – 30252(25-45) = -2030 – 40353(35-45) = -1040 – 50a =454(45-45) = 050 – 60553(55-45) = 1060 – 70651(65-45) = 20Why do we use this column to calculate the Mean instead of this one?Well, using this number set is a MINOR ADJUSTMENT to make calculations simpler, since the shift to the left by the ASSUMED MEAN ‘a’ is COMPENSATED by adding ‘a’ at the end of the calculation.What if we had the choice to simplify these numbers FURTHER? Would that make things a lot easier for us? Let us see how we can do that…Simplify ( –a) further?Do you notice a PATTERN? These numbers have a COMMON FACTOR of 10. Let the common factor be represented by lower case ‘h’. So we can say that ‘h’ is equal to 10. Also notice that ‘h’ is NOTHING BUT the length of the CLASS INTERVAL.Common Factor → h =10We could also say that these numbers DEVIATE in steps of 10 from ZERO. So we make these numbers SMALLER by dividing ‘ minus a’ by the COMMON FACTOR ‘h’. ‘h’ in our example is 10! = = Again this is JUST ANOTHER minor adjustment we are making to our to make calculations simpler. So we get a third set of numbers, -2, -1, 0, 1 and 2. These are known as STEP DEVIATIONS. So ‘ minus a’ gives us the DEVIATION; and ‘ minus a’ over ‘h’ gives us the STEP DEVIATION.Deviation → Step Deviation → Let us use a NEW VARIABLE to represent the STEP DEVIATIONS. So is EQUAL to ‘ minus a’ over h. = So we add another column for the STEP DEVIATIONS, .Class intervalxifi(xi -a)di = (xi-a)/h20 – 30252-20-230 – 40353-10-140 – 504540050 – 6055310160 – 70651202Notice that taking the step deviations results in a change of scale.Change of scaleThe DIFFERENCE here is 1 unit and the DIFFERENCE here is ‘h’ units or in our case 10 units. We can see that this set of numbers is smaller and simpler to handle than this set of numbers.The scale has REDUCED from 10 to 1, thereby making our deviations small.So what have we done with ALL our’s so far? We have SHIFTED the values of our ’s to the LEFT by the ASSUMED MEAN ‘a’ and then SCALED DOWN the shifted or DEVIATED values by h.Shifted left by ‘a’ units and scaled down by ‘h’We have ADJUSTED our ’s for the purpose of SIMPLIFYING calculations, but how do we get them BACK? After all we are calculating the Mean for our values.So to get back our all we need is to SCALE UP these values by ‘h’ and then add ‘a’ to shift these values to the RIGHT. The formula would look something like this! = . h + a (2)We scale up by multiplying, and shift to the right by adding! This is an important concept. The table we have built so far is PARTIALLY complete. It is the ONLY telling us how we can get to our STEP DEVIATIONS using our . We are YET TO find the Mean using these values.We still have one more column to be added before we can proceed towards calculating the Mean using the Step Deviation Method.We will continue building this table and apply this formula in our next video…Outline:WeExplain how the Assumed Mean Method simplifies calculations(in brief)We introduce the concept of Step DeviationsWe build a table with column to find the step Deviations

Table of Contents Mean using the Step Deviation Method – Part 1 Summary: We understand what Step Deviations are. We […]

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