Submitted by Editor
In our daily life, we have to collect facts which help us in answering most of the questions concerning the world in which we live. The facts we collect are often number facts such as the number of runs scored by Indian team against Pakistan.
The methods and techniques of collection, presentation, analyses and interpretations of numerical data in a logical and systematic manner so as to serve a purpose is known as ‘statistics’.
Statistics is a mathematical science pertaining to the collection, analysis, interpretation and presentation of data.
MEANING OF STATISTICS
Statistics is concerned with scientific method for collecting and presenting, organizing and summarizing and analyzing data as well as deriving valid conclusions and making reasonable decisions on the basis of this analysis.
ORIGIN AND GROWTH OF
STATISTICS (history)
The word ‘statistics’ and ‘statistical’ are derived from the Latin word status, means political state.
FUNDAMENTAL CHARACTERSTICS OF STAISTICS
SUB TOPICS
SOME RELATED DEFINATIONS
These fig. are in the ascending order
4,5,8,18,28,29,29,31,40,40,43,43,46,46,46,47,47,50,50,55,55,70,71,75,75,80,90
Marks | no. of students | Marks | No. of students |
4 | 1 | 46 | 3 |
5 | 1 | 47 | 2 |
8 | 1 | 50 | 2 |
18 | 2 | 55 | 3 |
28 | 1 | 70 | 1 |
29 | 2 | 71 | 1 |
31 | 1 | 75 | 2 |
40 | 2 | 80 | 1 |
The above data in the ascending order is called an ‘arrayed’ and the way of arrangement is called an ‘array’.
The way of arrangement of data in the table is known is known as ‘frequency distribution’.
Marks are called “variates” the no. of students who secured a particular no. of marks are frequency of variates is called “frequency of the variate”.
The number of times a number has been repeated is called the “frequency of the variate”.
CONTINOUS: Quantities which can take all numerical values within a certain interval .
DISCONTINOUS: Quantities or variable which can take only a finite set of values.
Each groups into which a raw data is condensed is called a “class”. The size of class is known as the “class interval”.
For ex. 10 is the class interval of class “0-10”.
Each class is bounded by 2 fig. which are called the “lower limits “and “20”is the “upper limit”.
The difference between the upper limit of the class and the lower limit of class is called as the “class size”.
The value which lies midway between lower and upper limits of a class is known as its “mid value or class mark”.
Class mark = upper limit + lower limit
2
The difference between the two extreme observations in an arranged data i.e. the difference between the maximum and minimum values of observations is known as the “Range”.
Three measures of central tendency are
MEAN
Median of groped data :if x1,x2 , x3 ,……….xn are variables of a variable x , then the arithmetic mean or simply mean of these values is denoted by X and is defined as X= x1 +x2 +x3 +……xn
n
or X= i=1n xi/n
ALGORITHM:
Step I= Prepare the frequency table in such a way that its first column consists of the values of the variate and the second column the ∑
Step II=multiply the frequency of each row with the corresponding values of variable to obtain third column containing fix;
Step III= Find the sum of all entries in column III to obtain ∑fixi. Step IV= Find the sum of all the frequencies in column II to obtain ∑fi= N
Step V= Use the formula: X = ∑fixi/N
For Ex= Find the missing frequencies in the following frequency distribution if it is known that the mean of the distribution is 1.46 No. of accidents (x): 0 1 2 3 4 5 Total
Frequency (f): 46 ? ? 25 10 5 200
COMPUTATION OF ARITHMATIC MEAN
Xi | fi | fixi |
0 | 46 | 0 |
1 | f1 | f1 |
2 | f2 | 2f2 |
3 | 25 | 75 |
4 | 10 | 40 |
5 | 5 | 25 |
∑f = N = 86+f1+f2 ∑f1x1=140+f1+2f2
N= 200
Also, Mean=1.46 -----------------------------------------------------------1
Solving 1,2
STEP DEVIATION METHOD
Step I- Obtain the frequency distribution and prepare the frequency table in such a way that its first column consists of the values of the variable and the second column corresponding frequencies.
Step II- Choose a number ‘A’(generally known as the assumed mean) and take deviations di=xi-A about A. Write these deviations against the corresponding di’s in the IV column.
Step IV- Multiply the frequencies in second column with the corresponding ui’s in IV column to prepare V column of fiui.
Step V- find the sum of all entries in V column to obtain (∑ni=1 fixi) and the sum of all frequencies in column to obtain N=(∑ni=1fi). Use formula:X=A+h{1/N fixi}
MEDIAN
The median is the middle value of a distribution is the value of the variable which divides it into two equal parts.
Step I-Arrange the observation x1,x2,………..xn in ascending or descending order of magnitude.
Step II- Determine the total no. of observation, say, n.
Step III- If n is odd , then median is the value of (n+⅟2) observation.
For ex.-Calculate the median from the following distribution:
Class: 5-10 10-15 15-20 20-25 25-30
Frequency: 5 6 15 10 5
30-35 35-40 40-45
4 2 2
SOLUTION: First cumulative table to complete median.
CLASS | FREQUENCY | CUMULATIVE FREQUENCY |
5-10 | 5 | 5 |
10-15 | 6 | 11 |
15-20 | 15 | 26 |
20-25 | 10 | 36 |
25-30 | 5 | 41 |
30-35 | 4 | 45 |
35-40 | 2 | 47 |
40-45 | 2 | 49 |
SO,
N=49 & N/2=24.5→The cumulative frequency just greater than N/2 is 26 and corresponding class is 15-20
(Median class) L=15, f=15, F=11, h=5
:. Median = (l+N/2-F)/f= 15+24.5-11/15*5 =19.5
MODE
The mode or modal value of a distribution is that value of the variable for which the frequency is maximum. In order to compute the mode of a series of individual observations. We first convert it into a discrete series frequency distribution by preparing a frequency table. From the frequency table, we identify the value having maximum frequency. The value of variable to obtain is the mode or modal value.
FOR EX.
Obtain the value of the following:
l → lower limit
h → width
fx → frequency
f1 → frequency of the class preceding
f2 → frequency of the class following.
MODE= l+(f-f1)/(2f-f1f2) * h
Relationship among mean, median and mode
MODE= 3median – 2mean
OR MEDIAN = mode+⅔ (mean – mode)
OR MEAN = mode + 3/2 (median – mode)
PIE-CHART
A pie – chart displays data as a percentage as a percentage of the whole Each pie has a label and percentage . A total data no. is included . These have a circle divided into parts or sectors of different sizes to show different amounts of data.
ADVANTAGES
DISADVANTAGE
BAR - GRAPH
A bar graph display data in separate columns. It data is on a continous scale, such as height, the bars touch each other. The bars can be vertical or horizontal.
ADVANTAGE
DISADVANTAGE
LINE GRAPH
A line graph plots continuous data as points and then joins them with a line. Multiple data sets can be grouped together, but a key must be used.
ADVANTAGES
DISADVANTAGE
Run Rate Graph
LINE GRAPH
HISTOGRAM
A histograph displays continuous data in order column. Categories are of continuous measures such as time, inches, temperature, etc.
ADVANTAGES
DISADVANTAGES
HISTOGRAM
Uses and applications of
statistics
Statistics and its studies have been used to answer questions such as:-
INDUSTRIES AND BUSINESS
AGRICULTURE
FORESTERY
EDUCATION
ECOLOGICAL STUDIES
MEDICAL STUDIES
SPORTS
Conclusion
Statistics has been a great learning experience and is a very interesting experience and an important topic that is very-very helpful for people of all ages and for teacher to clear their concept and increase their intelligence level.
0 Comments:
If opportunity doesn't knock, build a door. - Milton Berle