Formula for calculating mean median and mode data interpretation
Answers
Answer:
the mean median and mode are known as measures of central tendency. They are also known as statistical averages. Their simple function is to mathematically represent all the values in a particular set of data. Hence, this representation shows the general trend and inclination of all the values.
n and Mode.
Arithmetic Mean
Mean = ∑X ÷ N
Mean Calculation for Individual Series
1. Direct Method
In this method, the formal definition of mean is used. The values of items are simply summed and divided by the number of observations.
Mean=∑X÷N
2. Assumed Mean Method
In the assumed mean method, a value is randomly selected as an assumed mean.
formula:
Mean= A + (∑d÷N)
Here, A= Assumed value of the mean
∑d= Summation of deviations and N= Number of observations
3. Step Deviation Method
Similar to the assumed mean method, the concept behind step deviation method is to make calculations easier. It is a simpler variant of the assumed mean method and is used when there is a common factor among all the deviations by which they can be divided to reduce their values.
The factor is indicated by ‘C’. The deviation, when reduced by this factor, is known as a step-deviation. The formula is as follows:
Mean = A + (∑fd’/∑f)×C
C = The common factor using which deviations are converted to step-deviations
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
Step-by-step explanation:
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