CENTRAL TENDENCY....................pptx

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1. CENTRAL TENDENCY

2. Introduction :- Central tendency or central position or statistical averages or measures of location reflects the central point or the most characteristic value of a set of measurements - denoted by Mean, Median, and Mode.

3. Arithmetic mean is a mathematical average and it is the most popular measures of central tendency. It is frequently referred to as ‘mean’ it is obtained by dividing sum of the values of all observations in a series (ƩX) by the number of items (N) constituting the series. Thus, mean of a set of numbers X1, X2, X3,………..Xn denoted by x ̅ and is defined as

4. It is easy to understand & simple calculate. It is based on all the values. It is rigidly defined . It is easy to understand the arithmetic average even if some of the details of the data are lacking. It is not based on the position in the series.

5. It is affected by extreme values. It cannot be calculated for open end classes. It cannot be located graphically It gives misleading conclusions. It has upward bias.

6. Key points:- Since mean is calculated by taking into account all observations, it can be subjected to statistical tests (tests of significance). Mean is the only statistical average, where statistical analysis can be undertaken unlike median and mode, which is its greatest advantage. The only disadvantage is that, mean is affected by extreme values (outlier). Thus mean is said to be a sensitive measure. So in case of extreme value in an observation, mean

7. Median Median is the value that divides the series into two equal groups, so that half of the values are greater than and half are less than median. Thus median is the point or value on either side of which 50% of the distribution falls and it is denoted as 'Me’. It is a better indicator of central value, when one or more of the lowest or the highest observations are wide apart or not so evenly distributed, e.g. age at marriage, duration of stay in hospital and incubation period of leprosy, since these are wide and variable. Thus median is said to be one of the robust measure of central tendency

8. CONT … Median is neither dependent on number of observations and nor dependent on distribution of observations. At first data are arranged in ascending or descending order of magnitude and then the value of middle observation is located, which is called median. In case of an odd number of observations, the middle most value is taken, while for an even number of observations, average of two middle values is taken.

9. There is an alternate way to find the median value for odd number of observations : Then median for odd number of observations = [(n + 1) / 2] th value; while n is total number of observations. In the above example, n = 9, so (9+1)/2 = 5 th value Alternate method of determining median value for even number of observations : Average of (n / 2) th and [(n / 2) + 1] th value in the series; n being the number of observations. lf n= 10, then average of 5th and 6th value will be the median.

10. Advantages of Median: Median can be calculated in all distributions. Median can be understood even by common people. Median can be ascertained even with the extreme items. It can be located graphically It is most useful dealing with qualitative data

11. It is not based on all the values. It is not capable of further mathematical treatment. It is affected fluctuation of sampling. In case of even no. of values it may not the value from the data.

12. Mode is the most frequent value or score in the distribution. It is defined as that value of the item in a series. It is denoted by the capital letter Z. highest point of the frequencies distribution curve .

13. Mode is readily comprehensible and easily calculated It is the best representative of data It is not at all affected by extreme value. The value of mode can also be determined graphically. It is usually an actual value of an important part of the series.

14. 🞂 ​ It is not based on all observations. 🞂 ​ It is not capable of further mathematical manipulation. 🞂 ​ Mode is affected to a great extent by sampling fluctuations. 🞂 ​ Choice of grouping has great influence on the value of mode .

15. A measure of central tendency is a measure that tells us where the middle of a bunch of data lies. Mean is the most common measure of central tendency. It is simply the sum of the numbers divided by the number of numbers in a set of data. This is also known as average.