Question

Write the formula to find mean median and mode of any given data also explain median in case of odd and even number of terms

Answer 1

please mark me brainlist



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. Generally, the value is around the centre of the series as this facilitates calculations( the calculated deviations are both negative and positive around the assumed value, hence they cancel out or sum up to a very small value).

The assumed mean is found by dividing the maximum and minimum values by 2. Now deviation of each value from the assumed mean is calculated as deviation = value of the item – assumed value of mean in a separate column. The summation of these deviations are calculated and actual mean is derived using the given formula:

Mean= A + (∑d÷N)
l

Mean Calculation for Discrete Series
Again in case of discrete series, mean can be calculated by three approaches as follows:

1. D




Here, X = The value of the item, A = Assumed value of mean and

C = Common factor chosen

Mean Calculation for Frequency Distribution
The three approaches towards calculating mean for frequency distribution series are as follows:

1. Direct Method
In a frequency distribution, instead of individual values of observations, classes are mentioned. Hence to find the mean we need a single value that can represent the interval.

Such a value is found by adding the upper and lower class values and dividing the sum by 2. This value is known as mid-value. It is usually represented by m or Xi.

2. Assumed Mean Method
The overall idea of the assumed mean method here also remains the same except the fact that the concept of mid values is incorporated. The formula remains the same as the following:
.

3. Step-Deviation Method
Since the assumed mean method, in this case, is almost the same, likewise, the step deviation method also remains almost the same as it is a simpler version of the former. The only change incorporates the concept of mid-values. The formula is as follows:
Mean = ∑WX/∑W

Here, ∑WX = Summation of the product of items and the corresponding weights assigned to them

∑W = Summation of the weights

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..

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 i

Answer 2

Hello,
1. Mean=sum of all observations/no. Of observations
2. Mode =(the mode of a set of observations that occurs most often is the mode of the give data)
3. Median =) step 1.arrange the given data I. Ascending order
Step 2. ((No. Of observations) /2) =) even
Step 2. For odd=) (no. Of obs. +1/2)
Thanks
Pls mark it if helped