MODE.pptx

Introduction to Mode.
Calculation of modes by different methods.
Merits and Demerits of Mode.
Mode is the value which occurs the maximum number of times in a series of observations and has the highest frequency.
Calculation of Mode
1. Calculation of mode in a series of individual observations (Ungrouped data)
2. Calculation of mode in a discrete series (Grouped data)
3. Calculation of mode in a continuous series (Grouped data)
4. Calculation of mode in a unequal class intervals (Grouped data)

1. BIOSTATISTICS AND RESEARCH METHODOLOGY Unit-1: mode PRESENTED BY Gokara Madhuri B. Pharmacy IV Year UNDER THE GUIDANCE OF Gangu Sreelatha M.Pharm., (Ph.D) Assistant Professor CMR College of Pharmacy, Hyderabad. email: [email protected]

2. MODE It is a value which occurs the maximum number of times in a series of observations and has the highest frequency. This value of the variable at which the curve reaches a maximum is called the mode. Mode is the easiest to calculate since it is the value corresponding to the highest frequency. It is derived from the French word “La mode’’ which means fashion. However according to croxton and cowden , “The mode of a distribution is the value at the point around which the items tend to be most heavily concentrated’’. It may be regarded as the typical value of series of values. A set of data may have a single mode , in which the case it is said to be unimodal. When concentration of data occurs at two or more points, such a series is called bimodal or multimodal, depending on the number of such points. Example: RBCs number of 15 patients of a hospital were recorded as 30,32,33,31,35,37,40,36,39,36,34, 36,35,41 and 38 Lac/ mm 3 . Solution: Arrange the data in ascending order and prepare a frequency distribution table. Since the item 36 appears maximum number of times, i.e., 3times. Therefore , 36 is the value of mode in the series. Since the item 36 appears maximum number of times, i.e , 3 times . Therefore, 36 is the value of mode in the series

3. Calculation of Mode Calculation of mode in a series of individual observations (Ungrouped data) Calculation of mode in a discrete series (Grouped data) Calculation of mode in a continuous series (Grouped data) Calculation of mode in a unequal class intervals (Grouped data)

4. 1) Calculation of mode in a series of individual observations Mode can be ascertained by mere inspection in case of individual observations. The values occurring the maximum number of times are the modal class. Example: Find the mode of the following data relating to the weights of 10 patients. Solution: Since the item 11 occurs the maximum number of times i.e., 4 times, the modal values is 11. If two values have the maximum frequency, the series is bimodal. Weight(kgs) 1 2 3 4 5 6 7 8 9 10 Number of patients 10 11 10 12 13 11 9 8 11 11 Weight(kgs) 8 9 10 11 12 13 Number of patients 1 1 2 4 1 1

5. 2) Calculation of mode in a discrete series Mode can be determined by looking to that value of the variable around which the items are most heavily concentrated. Example: Find the mode of the following frequency distribution of the weights of the 10 tablets Solution: we find out the value 11 of the variable x occurs maximum numbers of times, i.e. 15. But we notice that the difference between the frequencies of the values of the variable on both sides of 15, which are very close to 11 is very small. This shows that the variable x are heavily concentrated on either side of 11. therefore , if we find mode just by inspection, an error is possible. This problem is solved by the method of grouping as it is an irregular distribution in the sense that the difference between maximum frequency 15 and frequency preceding it is very small. Let us prepare the grouping and analysis table. Size(x) 4 5 6 7 8 9 10 11 12 13 Frequency(f) 2 5 8 9 12 14 14 15 11 13

6. Size(x) Frequency(f) Col. Of two Col. Of two leaving the first(iii) Col. Of three (iv) Col. Of three leaving the first (v) Col. Of three leaving the first two (vi) 4 5 6 7 8 9 10 11 12 13 2 5 8 9 12 14 14 15 11 13 7 17 26 29 34 13 21 28 26 15 35 40 22 40 39 29 43

7. ANALYSIS TABLE X Col. no 4 5 6 7 8 9 10 11 12 13 i 1 ii 1 1 iii 1 1 iv 1 1 1 v 1 1 1 vi 1 1 1 Total frequency 1 3 5 4 1 But by inspection one is likely to say that the modal value is 11, since it occurs the maximum numbers of times, i.e., 15, which is incorrect as revealed by analysis and grouping table which gives the correct modal value as 10 (though it occurs 14 times).

8. 3) Calculation of mode in a continuous series Modal class : it is the class in a groped frequency distribution in which the mode lies. This modal class can be determined either by inspection or with the help of grouping table. After finding the modal class , we calculate the mode by the following formula. Mode = Where = the lower limit of the modal class i = the width of the modal class = the frequency of class preceding the modal class = the frequency of the modal class = the frequency of the class succeeding the modal class Sometimes, it so happened that above formula fails to give the mode. In this case, the modal value lies in a class other than the one containing maximum frequency. In such cases, we take the help of the following formula Mode = Where, =  

9. Example: Find the mode of the following data Solution: From the above table, it is clear that the maximum frequency is 32 and it lies in the class 16 – 20. Thus modal class is 16 – 20 Here = 16 , = 32, = 16, = 24, i = 5 Mode = = = 16 + 3.33 = 19.33   Clinical trial frequency 1 - 5 6 - 10 11 - 15 16 - 20 21 - 25 No of patients 7 10 16 32 24

10. 4) Calculation of mode in unequal class intervals Before we compute the mode in unequal class –intervals, the class-intervals should be made equal and frequencies should be adjusted accordingly. Example: calculate the mode of the following distribution: Solution: In this problem the class-intervals are unequal, therefore, we must adjust the frequencies and make the class-intervals equal. mode lies in the class = 130 – 140 mode = L = 130, ∆ 1 =(27 -20) = 7 , ∆ 2 = (27 – 17) = 10, i = 10 mode = = 130 + = 130 + 4.12 Mode = 134.12   No of tablets 100 - 110 110 - 130 130 - 140 140 - 160 160 - 170 170 - 180 No of capsules 11 40 27 34 12 6 No of tablets No of capsules 100 - 110 11 110 - 120 20 120 - 130 20 130 - 140 27 140 - 150 17 150- 160 17 160 - 170 12 170 - 180 6

11. Merits of Mode Mode is easy to calculate and can be determined by a mere observation of the data. The mode is not unduly affected by extreme items It is simple and precise Mode is the point where there is no more concentration of frequencies. Hence , it is the best representative of the data. Demerits of Mode The mode is not based on all the observations. The value of the mode cannot be determined in bimodal distribution . It is not a rigidly defined measure. Sometimes the exact value of the modal class cannot be known by inspection of the data. Therefore it is necessary to prepare grouping table and then an analysis table to find out the modal class