Question

The three methods of finding mean​

Answer 1

Answer---♂♀

● DIRECT METHOD.

◆ This is the shortest and simplest method to calculate the arithmetic mean of a grouped data set. The steps are as follows

◆ Prepare a table containing four columns.

◆ In column 1 write the class interval.

◆ In column 2 write the corresponding class marks (midpoint of the class interval) denoted by xi

◆ In column 3 write the corresponding frequencies (fi) of the class intervals

◆ In column 4 write the product of column 2 and column 3 which is denoted by xifi

◆ Calculate Mean by the Formula Mean = ∑xifi / ∑ fi

● ASSUMED MEAN METHOD.

◆ Also called the shift of origin method, this method is used when the calculation by the direct method becomes very tedious. Steps to be followed are :-

◆ Prepare a table containing five columns

◆ Write the class intervals in column 1

◆ Write the corresponding class marks in column 2, denoted by xi.

◆ Take the central value from amongst the class marks as the Assumed Mean denoted as A.

◆ In column 3 calculate the deviations, i.e. di = xi – A

◆ In column 4 write the frequencies (fi) of the given class intervals

◆ In column 5 find the mean of di using formula Mean of di = ∑xidi / ∑ di

◆ To finally to calculate the Mean, we add the assumed mean to the mean of the di

● STEP DEVIATION METHOD.

◆ This is also called the shift of origin and cale method. Steps to be followed are

◆ Prepare a table containing five columns

◆ Write the class intervals in column 1

◆ Write the corresponding class marks in column 2, denoted by xi.

◆ Take the central value from amongst the class marks as the Assumed Mean denoted as A.

◆ In column 3 calculate the deviations, i.e. di = xi – A

◆ In column 4 calculate the values of ui, ui= di/h, where h is the class width.

◆ In column 5 write the frequencies (fi) of the given class intervals

◆ Calculate the product of Column 4 and column 5, which is fiui

◆ Find the Mean of ui = ∑xiui / ∑ ui

◆ To find the mean we add the assumed mean A to the product of class width height (h) with mean of ui.♀

Answer 2

● DIRECT METHOD.

◆ This is the shortest and simplest method to calculate the arithmetic mean of a grouped data set. The steps are as follows

◆ Prepare a table containing four columns.

◆ In column 1 write the class interval.

◆ In column 2 write the corresponding class marks (midpoint of the class interval) denoted by xi

◆ In column 3 write the corresponding frequencies (fi) of the class intervals

◆ In column 4 write the product of column 2 and column 3 which is denoted by xifi

◆ Calculate Mean by the Formula Mean = ∑xifi / ∑ fi

● ASSUMED MEAN METHOD.

◆ Also called the shift of origin method, this method is used when the calculation by the direct method becomes very tedious. Steps to be followed are :-

◆ Prepare a table containing five columns

◆ Write the class intervals in column 1

◆ Write the corresponding class marks in column 2, denoted by xi.

◆ Take the central value from amongst the class marks as the Assumed Mean denoted as A.

◆ In column 3 calculate the deviations, i.e. di = xi – A

◆ In column 4 write the frequencies (fi) of the given class intervals

◆ In column 5 find the mean of di using formula Mean of di = ∑xidi / ∑ di

◆ To finally to calculate the Mean, we add the assumed mean to the mean of the di

● STEP DEVIATION METHOD.

◆ This is also called the shift of origin and cale method. Steps to be followed are

◆ Prepare a table containing five columns

◆ Write the class intervals in column 1

◆ Write the corresponding class marks in column 2, denoted by xi.

◆ Take the central value from amongst the class marks as the Assumed Mean denoted as A.

◆ In column 3 calculate the deviations, i.e. di = xi – A

◆ In column 4 calculate the values of ui, ui= di/h, where h is the class width.

◆ In column 5 write the frequencies (fi) of the given class intervals

◆ Calculate the product of Column 4 and column 5, which is fiui

◆ Find the Mean of ui = ∑xiui / ∑ ui

◆ To find the mean we add the assumed mean A to the product of class width height (h) with mean of u

Explanation:

Explanation:

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