/2018 -2019Lecture2/Frequency Distrlbufions and Measures of Central Tendency

Frequency Distributions.
When observations, discrete or continuous, are available on a single characteristic of a large number of individuals, often it becomes necessary to condense the data as far as possible without losing any information of interest.
Example
Let us consider the marks in statistics obtained by 250 candidates selected at random from among those appearing in a certain examination•.
TABLE 1: Marks in Statistics of 250 Candidates
32 47 41 51 41 30 39 18 48 53 18 53 68-15=53=Range
54 32 31 46 15 37 32 56 42 48 56 If we choose
38 26 50 40 38 42 35 22 62 51 22 62
44 21 45 31 37 41 44 18 37 47 21 47
68 41 30 52 52 60 42 38 38 34 30
41 53 48 21 28 49 42 36 41 29 21 53
30 33 31 35 29 37 38 40 32 49 29 49
43 32 24 38 38 22 41 50 17 46 17 46
46 50 26 15 23 42 25 52 38 46 15 52
41 38 40 37 40 48 45 30 28 31 28 48
40 33 42 36 51 42 56 44 35 38 33 56
31 51 45 41 50 53 50 32 45 48 31 50
40 43 40 34 34 44 38 58 49 28 28 58
40 45 19 24 34 47 37 33 37 36 19 47
36 32 61 30 44 43 50 31 38 45 31 61
46 40 32 34 44 54 35 39 31 48 31 48
48 50 43 55 43 39 41 48 53 34 34 55
32 31 42 34 34 32 33 24 43 39 24 43
40 50 27 47 34 44 34 33 47 42 27 47
17 42 57 35 38 17 33 46 36 23 17 57
48 50 31 58 33 44 26 29 3t 37 26 58
47 55 57 37 41 54 42 45 47 43 37 57
37 52 47 46 44 50 44 38 42 19 19 52
52 45 23 41 47 33 42 24 48 39 23 52
48 44 60 38 38 44 38 43 40 48 34 48
68-15=53=Range
If we choose the number of the class-intervals =11, then
Range/11=53/11=4.8181818181818181818181818181818?5=length of the interval
k. The classes of the type 15- 19,20-24,25-29 etc., in which 50 -54 26
both the upper and lower limits included are called inclusive intervals , the the following is the frequency table.