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 + ….. X_n

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 = 6^th 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/₂ – F_b   c where L₁ = The lower class boundary of the median

F            N = total frequency

F_b = cumulative frequency before the median class

F = Frequency of the median class

C = the size (width) of the median class