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

- Arithmetic mean

Detoned by X = __X _{1} + X_{2} + X_{3} + ….. X_{n}__

n

X = X_{1}

__1 = 1__ = __Ƹ____x__

n n

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

12,8,9,10,12

X = __Ԑ____x__

n

X = __12 + 8 + 9 + 10 + 12__ = __51__

5 5

X = 10.2

- Assume mean = A +
__Ԑ____d__

n

- 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

- Variance =
__Ԑ____(x – x)2__

n

- Standard deviation

S = __Ԑ(x – x)2__

n

- Mean of group data

X = A + ^{Ԑ}^{fd}/_{Ԑ}_{f}

- 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

- Median from group data

= L_{1} + __ ^{N}/_{2} – __F

_{b}c where L

_{1}= 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