Why do we mostly use step deviation method while finding mean in empirical formula of mean, median and mode?
Even books are using step deviation method.
Why don't we use assume mean method or direct method?
Answers
Answer:
etic Mean
Median
Another measure of central tendency i.e. (Mean Median and Mode) is median which is essentially known as the central value of a series. Median is a value in series such that it divides the series exactly in halves. This means one half of the series above median contains all values greater than it and the other half contains all values smaller than the median. Hence median is the mid-value.
Calculation of Median
Median for Individual series
In individual series, where data is given in the raw form, the first step towards median calculation is to arrange the data in ascending or descending order. Now calculate the number of observations denoted by N. The next step is decided by whether the value of N is even or odd.
If the value of N is odd then simply the value of (N+1)/2 th item is median for the data.
If the value of N is even, then use this formula: Median = [ size of (N+1)/2 term + size of (N/2 + 1)th term]÷2
Median for Discrete Series
The first step for calculation of median here also involves arranging the data in ascending or descending order. This is followed by conversion of simple frequencies into cumulative frequencies. Hence another column for cumulative frequency needs to be constructed, wherein the last value is labeled as the value of N (i.e ∑f).
Next, we need to find the value of (N+1)/2. Lastly, the value corresponding to the cumulative frequency just greater than (N+1)/2 is termed as the median for the data.
Median for Frequency Distribution
As in all other types of distributions, here also initially we arrange the classes in either ascending or descending order. Next, we need to find the cumulative frequencies. The last value in the cumulative frequency column which is ∑f is labeled as N. This is followed by the calculation of the value of N/2.
Further, the class corresponding to the cumulative frequency just greater than this value is known as the median class. Lastly, the median value is calculated by applying the following formula:
Median = l/2 + h/f [ N/2 – C]
Here, l = The lower limit of the median class
h = size of the class, f = Frequency corresponding to the median class
N = Summation of frequencies
C = The cumulative frequency corresponding to the class just before the median class
Mode
Now we come to the third concept of Mean Median and Mode. It is the measure of central tendency aims at pointing out the value that occurs most frequently in a series. This value, when it represents the data is known as the mode of the series. Mode simply refers to the value that occurs the maximum number of times in a distribution.
Calculation of Mode
Mode for Individual Series
In case of individual series, we just have to inspect the item that occurs most frequently in the distribution. Further, this item is the mode of the series.
Mode for Discrete Series
In discrete series, we have values of items with their corresponding frequencies. In essence, here the value of the item with the highest frequency will be the mode for the distribution.
Mode for Frequency Distribution
Lastly, for frequency distribution, the method for mode calculation is somewhat different. Here we have to find a modal class. The modal class is the one with the highest frequency value. The class just before the modal class is called the pre-modal class. Whereas, the class just after the modal class is known as the post-modal class. Lastly, the following formula is applied for calculation of mode:
Mode = l + h [(f1-f0)/(2f1-f0-f2)]
Here, l= The lower limit of the modal class
f1 = Frequency corresponding to the modal class,
f2 = Frequency corresponding to the post-modal class,
and f0 = Frequency corresponding to the pre-modal class
Answer:
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