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 = 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
- Assume mean = A + Ԑd
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 = 6th 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 + 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
- Median from group data
= L1 + N/2 – Fb 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