RELATION BETWEEN MODE, MEAN AND MEDIAN

The following question was asked in UPSC Civil Services IAS General Studies Question in 2004 Main Paper II: a)Which of the three averages -- arithmetic mean, median and mode, adequately represents the data? (b) In a moderately skewed distribution the following values were obtained:. Arithmetic mean = 24.6, Mode = 26.1 Find the value of the median and explain the reason for the method employed. To answer such type of question, you should know the meaning of mean,median and mode as well as the relation between them. ------------------------------------------------------------------ MEAN: It is JUST the average. For 2,3,4 the average is (2+3+4)/3=3 No more explanation is needed for Mean. -------------------------------------------------------------------- MEDIAN: It is the middle value. For 2,3,4 the Median is 3. Actually the steps involved is 1. you have to arrange alll the given numbers in ascending order 2. Then pickup the middle one. But what is the mean for 2,3,4,5? Here there is no middle number. So when the total numbers are Even, then take the TWO MIDDLE NUMBERS AND FIND THE AVERAGE. (3+4) / 2 = 3.5 ---------------------------------------------------------------------- MODE: It the value which is MOST FREQUENTLY occuring. What is the Mode in the series : 2,3,4,4, 5? Here 4 is occuring most frequently occuring. What is the MOde in the series: 2,3,3,4,4,5? Answer: 3,4 What is the Mode for 2,3,3,3,4,4,5? Answer : 3 What is the mode for 2,3,4,5? Answer 2,3,4,5 ----------------------------------------------------------------------- RANGE: is the difference between the highest value and lowest value. What is the range for the set 2,3,4,5? Answer 5-2=3 What is the range for the set 5,6,7? Answer 7 minus 5=2 ------------------------------------------------------------------------------------- Out of mean,mode, median, if any two are given you can find out the other. The formula is : 1 mode plus 2 mean = 3 median How to remember this formula? Step 1: You know 1 + 2 = 3 Step 2: So you have to remember the order:;MODE MEAN MEDIAN. You can say aloud this word "MO-MEA-MEDI" 100 times.  அவள் "மாமியா மடி" யில் தூங்கினாள்