5
.
Which measure of central tendency is used in the following situations?
(mean, median, mode)
i.
The amount you pay against electricity per month in a year.
The pharmacists to place order for a particular size of mask.
The average amount contributed by 50 families for Corona relief
fund.
Favourite subject of students of class IX.
Based on a rating given between numbers 1-5, by 10 audience,
a singer is selected if majority of the rating is 3 and above, else
rejected.
The team which has won the football championship most often
in the last 10 years.
Answers
Explanation:
Arithmetic Average (Mean):
Mean is calculated when data are complete and presented on equal interval scale. The arithmetic average or mean is quite simple and most widely used and is hence called ‘Common Average’ or even simply ‘Average’. It is a measure of central value. It is a method of representing whole data by one figure and takes into consideration all the items. Mean provides an accurate description of the sample and indirectly, that of population.
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It is the sum of measurements divided by their number. Mean of a distribution of scores may be defined as the point on the scale of measurement obtained by dividing the sum of all the scores by the number of scores.
In other words arithmetic mean is the sum of the separate scores or measures divided by their number. If a man earns Rs. 300, Rs. 400, Rs. 450, Rs. 500 and Rs. 550 on five successive days,his mean daily wage (Rs. 440) is obtained by dividing the sum of his daily earnings by the number of days he has worked.
The formula for the mean (M) of a series of ungrouped measures is:
where ∑ mean sum total of,
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N is the number of measures in the series,
X stands for a score or other measure.
Calculation of Mean from Ungrouped Data:
The arithmetic mean for ungrouped data can be calculated by using any of the following two methods:
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i. Direct method.
ii. Short-cut method.
(a) Direct Method:
In case of ungrouped data we are always given some measurements on a variable X say X1, X2, X3 ……………………… Xn are ‘n’ items then the arithmetic mean (x) of these items is equal to
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where x = Mean
n = No of items
X = Score