BAR CHART consists of rectangles all with the same width but with lengths proportional to the frequencies of the items on the data .
PIE CHART is a circle divided into sectors whose angles are proportional to the frequencies of the items. The angels are measured in order to obtain the frequencies.
2.Mean, Mode, and Median
MEAN: this is the most common kind of average. If there are numbers on a set then
Mean = sum of the number in the set divided by the total number of items in the set .
MEDIAN : this is when a set of numbers are arranged in order of size the middle term is the median . If there is an even number of terms the median is the arithmetic mean of the two terms.
MODE:the mode of a set of numbers is the number of tug the highest frequency.
3.Grouped Data
This is used to solve statistical data that contains the large number of values . It consists of ;
GROUPED FREQUENCY DISTRIBUTION: This is a table where the data are grouped in class intervals. The limit of class interval must be defined clearly.
CLASS LIMIT: They are the end values of each class interval.
CLASS BOUNDARIES: they are measured to the nearest whole number of each class interval for example;
Class interval:145-154
Class boundaries: 144.5-154.5
The lower class boundary (145 was changed to 144.5 by subtracting 0.5 ) while the upper class boundary( 154 was changed to 154.5 by adding 0.5)
CLASS WIDTH: this is the difference between the lower and upper class boundary for example;
Class boundaries: 144.4-154.5
Class width= 154.5-144.5
=10
CLASS MID-VALUE: this is the mid-point of the class interval for example:
Class interval: 145-154
Class mid-value: (145+154) =299
=299 divided by 2
= 149.5
HISTOGRAM: this consists of a number of rectangles. The horizontal width of each rectangle is given by the class width. The height is such that the area of the rectangle is proportional to the frequency in that interval.
4.Range, Mean Deviation, and Standard Deviation
MEAN DEVIATION: In mean deviation, if X1, X2, X3,....,Xn are the elements of the set of data , [x] denotes the mean, then the mean deviation is defined by ;
MD= sum of |X - [x] | divided by n( n is the total number of numbers in the set )
If X1, X2, X3,...Xi have frequencies F1, F2, F3,..., Fi respectively, then the definition of the mean deviation can be modified as;
MD= sum of Fi |x -[x] | divided by sum of Fi
When X is the class mark.
RANGE : the range of a set of numbers is the difference between the largest and smallest numbers in a set .
RANGE QUARTILE : the value of the variable axis which Sibiu the area of the histogram in the ratio 1:3 is called FIRST QUARTILE .(Q1)
The value of the variable axis which divides the area of the histogram in the ratio 3:1 is called THIRD QUARTILE (Q3)
The median coincides with the SECOND QUARTILE(Q2) which divides the area of the histogram into two equal parts .
The interquartile range = Q3- Q1
The semi-interquartile range =(Q3-Q2) divided by 2.
STANDARD DEVIATION: Variance is a single value which gives a convenient measure of dispersion of a distribution. Variance is the mean of the squares if the deviation from the mean . Thus ;
Variance= sum of d^2 ( d squared) divided n ( total number in the set)
OR
Variance= sum of (x-m)^2 divided by n
d is the deviation which states
d=x-m
X stands for each number
M stands for the mean
N stands for total number in the set
Stigma sign stands for sum of
Standard Deviation = square root of variance
5.Probability
Probability is the likelihood of a desired event happening. We can conclude that ;
Probability = number of required data outcomes divided by the total number of possible outcomes.
P(S)= n(S) divided by n(Ę)
P(S) is the probability of event occurring.
ADDITION LAW: If events A,B,C,... are mutually exclusive, the probability of A or B or C or , ... happening is the sun of the individual probabilities;
P(A) + P(B) + P(C) +......
PRODUCT LAW: If events A,B,C,... are independent, the probability of A and B and C and ..... happening is the product of there individual probabilities;
P(A) x P(B) x P(C) x....
FOR AN EVENT NOT TO HAPPEN:
The probability of an event not happening is p’ where p’= 1-p
P(A’)= 1-P(A)