2.1.4.2. Indirect Method

For a large number of observations, the indirect method is normally used to compute the mean. It helps in reducing the values of the observations to smaller numbers by subtracting a constant value from them.

The indirect method is frequently utilized when dealing with a large dataset to calculate the mean effectively. The core idea is to simplify the data by transforming the original values into smaller numbers. This is done by selecting a specific value (known as a constant) and subtracting it from each observation, allowing for easier calculations.

Imagine you are counting the number of pages in several thick books. Instead of counting each page, you decide that each book starts from 100 pages, and you will just note how many more pages each book has beyond that. This is similar to the indirect method, where you simplify a complex task to make it more manageable.

For example, as shown in Table 2.1, the rainfall values lie between 800 and 1100 mm. We can reduce these values by selecting ‘assumed mean’ and subtracting the chosen number from each value. In the present case, we have taken 800 as assumed mean. Such an operation is known as coding.

To illustrate the indirect method, let's consider a dataset of rainfall measurements ranging from 800 mm to 1100 mm. We can pick a value, in this case, 800 mm, as the 'assumed mean.' By subtracting 800 from each recorded rainfall value, we are effectively coding the data. Coding reduces the complexity of the observations and makes subsequent calculations simpler.

Think of coding as adjusting the starting point of a race. If a runner begins 800 meters ahead, every distance they run after that is more about their performance rather than starting from zero. Coding helps to redefine the context of data to make it easier to analyze.

The following formula is used in computing the mean using the indirect method: X = A + ∑d / N Where, A = Subtracted constant ∑d = Sum of the coded scores N = Number of individual observations in a series.

The mean, when calculated using the indirect method, is derived from a specific formula. In this formula, 'X' represents the mean, 'A' is the constant we subtracted (the assumed mean), '∑d' is the total of all coded values, and 'N' is the total number of observations. By plugging in these values into the formula, we can accurately determine the mean of the dataset.

Consider you own a bakery and have a set of sales data showing how many pastries are sold each day. Instead of looking at each day’s sales individually, you use a discount of 10 pastries. At end-of-the-month, you find the average number of pastries sold (as if you started from this new baseline). The formula would help you efficiently calculate the average sales without getting lost in all the daily figures.

Mean for the data as shown in Table 2.1 can be computed using the indirect method in the following manner: X = 800 + 884 / 7 = 800 + 126.29 = 926.29 mm. Note that the mean value comes the same when computed either of the two methods.

Using the data presented, where 884 is the total of the coded scores and 7 is the number of observations, we apply the formula to calculate the mean. When you add the assumed mean of 800 with the average of the coded observations (which is 126.29), the result gives us 926.29 mm as the final mean rainfall measured. Moreover, it's important to note that regardless of the method used, the mean remains the same, verifying the reliability and accuracy of both approaches.

If afterward, your bakery averaged 926 pastries sold when accounting for that discount, it would serve as a confirmation that both methods of measuring (actual sales vs. adjusted sales) give consistent results. This consolidation of methods is vital in ensuring reliability in statistical reports.

--