Random Sample Statistics
Random sample statistics:-
Random sample statistics deal with the population , sample and random sampling.
Population: is the total set of observations.
Sample : it is a part of the population. We call it subset of the population.
Parameter is the measurable characteristic of a population. Ex: mean or standard deviation.
Statistic is a measurable characteristic of the sample. It could be mean or standard deviation.
A sampling method is the procedure for selecting sample elements from a population.
A random number is a number chosen by chance.There is no formula for choosing it..
A random number table is a list of numbers. Numbers in the list are nor arranged in any order.
Properties of Random Sample Statistic:-
Random sample statistics are usually done in big shops where the population is a mixed one. The cinema hall, the public gardens, the shopping streets are all a good place to do random samplestatistics, where the population is a mixture of the rich, the middle class and the poor, the adults and the children, the seniors and the juniors, the sellers as well as the buyers.
The sampling is done at random, just a chance of sampling.
But there are certain properties .
* The population consists of N objects.
* The sample consists of n objects.
* All possible samples of n objects are equally likely to occur.
Types of Random Sample :-
Random sample statistics has many types of random sample.
1. A Simple random sample is selected so that all samples of the same size have an equal chance of being selected from the population. Simple random samples are self-weighting.
2. Stratified sampling:- involves selecting independent samples from a number of sub-populations, groups or strata from within a population. For ex: a sample of students, a sample of workers, a sample of breadwinners from the same population.
3. Cluster sampling :- involves seleting the sample units in groups. Units in the same cluster are likely to be more similar than two units picked at random.
These sampling are done to collect infromations about the various objects and analyse the informations so that a good decision can be taken on the subject that was analysed.
Random Sample Statistics:- Problem
Let us see some random sample statistics:-
* Before the actual polls, some of the well known magazine conduct a random sample statistics just to know the how the poll results would be. They select just a thousand people from various cities and towns and the information gathered would be analysed to know the heart beat of the total population.
*Manufacturers of consumer goods take a random sample statistics from a small group of people to know the effect of their goods in the market.
* Saalariesof the people in a town can be estimated using random sample statistics.
# In a certain town a random sample of executives have the following income in thousands.
35,43,29,55,63,72,28,33,36,41,42,57,38,30.
Compute point estimates for the mean and standard deviation of the incomes of the executives in the town.
Solution:-
Sep1 : let us find the mean of the 14 numbers:- 28+29+30+33+35+36+38+41+42+43+55+57+63+72=602
Step 2 : Mean = 602 14 = 43
Step 3 Let us find the variance.
__________________________
x x - AM (x - AM)2
__________________________
28 28 - 43 =-15 (-15)2 = 225
29 29 - 43 =-14 (-14)2 =196
30 30 - 43 = -13 (-13)2 =169
33 33 - 43 = -10 (-10)2 =100
35 35 - 43 = - 8 (-8)2 = 64
36 36 - 43 = - 7 (-7)2 = 49
38 38 - 43 = -5 (-5)2 = 25
41 41 - 43 = -2 (-2)2 = 4
42 42 - 43 = -1 (-1)2 = 1
43 43 - 43 = 0 0 = 0
55 55 - 43 = 12 122 = 144
57 57 - 43 = 14 142 = 196
63 63 - 43 = 20 202 = 400
72 72 - 43 = 29 292 = 841
_____ _____ _______
602 0 2 414
_____ ______ _______
Step 4 : Let us calculate variance = (x-AM)2 14 = 344.86
Step 5 : Let us now calculate the standard deviation: sq.rt of 344.86 = 18.6
Hence the arithmetic mean is 43 and standard deviation is 18.6
Thus we could say that the random sample statistics gives the salary of an average person in the town as $43,000 with a deviaton of 18.6
Random sample statistics deal with the population , sample and random sampling.
Population: is the total set of observations.
Sample : it is a part of the population. We call it subset of the population.
Parameter is the measurable characteristic of a population. Ex: mean or standard deviation.
Statistic is a measurable characteristic of the sample. It could be mean or standard deviation.
A sampling method is the procedure for selecting sample elements from a population.
A random number is a number chosen by chance.There is no formula for choosing it..
A random number table is a list of numbers. Numbers in the list are nor arranged in any order.
Properties of Random Sample Statistic:-
Random sample statistics are usually done in big shops where the population is a mixed one. The cinema hall, the public gardens, the shopping streets are all a good place to do random samplestatistics, where the population is a mixture of the rich, the middle class and the poor, the adults and the children, the seniors and the juniors, the sellers as well as the buyers.
The sampling is done at random, just a chance of sampling.
But there are certain properties .
* The population consists of N objects.
* The sample consists of n objects.
* All possible samples of n objects are equally likely to occur.
Types of Random Sample :-
Random sample statistics has many types of random sample.
1. A Simple random sample is selected so that all samples of the same size have an equal chance of being selected from the population. Simple random samples are self-weighting.
2. Stratified sampling:- involves selecting independent samples from a number of sub-populations, groups or strata from within a population. For ex: a sample of students, a sample of workers, a sample of breadwinners from the same population.
3. Cluster sampling :- involves seleting the sample units in groups. Units in the same cluster are likely to be more similar than two units picked at random.
These sampling are done to collect infromations about the various objects and analyse the informations so that a good decision can be taken on the subject that was analysed.
Random Sample Statistics:- Problem
Let us see some random sample statistics:-
* Before the actual polls, some of the well known magazine conduct a random sample statistics just to know the how the poll results would be. They select just a thousand people from various cities and towns and the information gathered would be analysed to know the heart beat of the total population.
*Manufacturers of consumer goods take a random sample statistics from a small group of people to know the effect of their goods in the market.
* Saalariesof the people in a town can be estimated using random sample statistics.
# In a certain town a random sample of executives have the following income in thousands.
35,43,29,55,63,72,28,33,36,41,42,57,38,30.
Compute point estimates for the mean and standard deviation of the incomes of the executives in the town.
Solution:-
Sep1 : let us find the mean of the 14 numbers:- 28+29+30+33+35+36+38+41+42+43+55+57+63+72=602
Step 2 : Mean = 602 14 = 43
Step 3 Let us find the variance.
__________________________
x x - AM (x - AM)2
__________________________
28 28 - 43 =-15 (-15)2 = 225
29 29 - 43 =-14 (-14)2 =196
30 30 - 43 = -13 (-13)2 =169
33 33 - 43 = -10 (-10)2 =100
35 35 - 43 = - 8 (-8)2 = 64
36 36 - 43 = - 7 (-7)2 = 49
38 38 - 43 = -5 (-5)2 = 25
41 41 - 43 = -2 (-2)2 = 4
42 42 - 43 = -1 (-1)2 = 1
43 43 - 43 = 0 0 = 0
55 55 - 43 = 12 122 = 144
57 57 - 43 = 14 142 = 196
63 63 - 43 = 20 202 = 400
72 72 - 43 = 29 292 = 841
_____ _____ _______
602 0 2 414
_____ ______ _______
Step 4 : Let us calculate variance = (x-AM)2 14 = 344.86
Step 5 : Let us now calculate the standard deviation: sq.rt of 344.86 = 18.6
Hence the arithmetic mean is 43 and standard deviation is 18.6
Thus we could say that the random sample statistics gives the salary of an average person in the town as $43,000 with a deviaton of 18.6
