Statistics of ungrouped data

Statistics is the practice or science of collecting and analyzing numerical data in large quantities, especially for the purpose of inferring proportions in a whole from those in a representative sample.

Meaning and statistics of mean, media, mode of ungrouped data

 

  1. Arithmetic mean

Detoned by X = X1 + X2 + X3 + ….. Xn

n

X = X1

1 = 1   = Ƹx

n         n

 

E.g. (1) Find the mean of the following set numbers

12,8,9,10,12

 

X = Ԑx

n

 

X = 12 + 8 + 9 + 10 + 12 = 51

5                      5

X = 10.2

 

  1. Assume mean = A + Ԑd

n

  1. Median = ½ (n + 1) where n members are arranged in order of magnitude

Example: Find the median 1,3,5,6,8,4,6,1,2,5 and 8

1,1,2,3,4,5,5,6,6,8,8, (arrange in ascending order)

½ (11 + 1)th

 

The median position = 6th member of the arranged set

:. The median = 5

 

  • Mode = The value that occurs most frequently
  1. Variance = Ԑ(x – x)2

n

  1. Standard deviation

S = Ԑ(x – x)2

n

  1. Mean of group data

X = A + Ԑfd/Ԑf

 

  • Median from frequency distribution

(N+1/2)th for odd number

(N/2)th + (N/2 + 1)th member for even number of items

2

  1. Median from group data

= L1 + N/2Fb   c where L1 = The lower class boundary of the median

F            N = total frequency

Fb = cumulative frequency before the median class

F = Frequency of the median class

C = the size (width) of the median class

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