statistics binomial distribution

This strategy for examining is utilized as a part of circumstance where the population can be effortlessly partitioned into gatherings or strata which are particularly not quite the same as one another, yet the components inside of a gathering are homogeneous regarding a few attributes e. g. understudies of school can be separated into strata on the premise of sexual orientation, courses offered, age and so forth. In this the population is initially partitioned into strata and afterward a basic irregular specimen is taken from every stratum. Stratified testing is of two sorts: proportionate stratified inspecting and disproportionate stratified examining.

  • Proportionate Stratified Sampling – In this the number of units selected from each stratum is proportionate to the share of stratum in the population e.g. in a college there are total 2500 students out of which 1500 students are enrolled in graduate courses and 1000 are enrolled in post graduate courses. If a sample of 100 is to be chosen using proportionate stratified sampling then the number of undergraduate students in sample would be 60 and 40 would be post graduate students. Thus the two strata are represented in the same proportion in the sample as is their representation in the population.

    This method is most suitable when the purpose of sampling is to estimate the population value of some characteristic and there is no difference in within- stratum variances.

  • Disproportionate Stratified Sampling – When the purpose of study is to compare the differences among strata then it become necessary to draw equal units from all strata irrespective of their share in population. Sometimes some strata are more variable with respect to some characteristic than other strata, in such a case a larger number of units may be drawn from the more variable strata. In both the situations the sample drawn is a disproportionate stratified sample.

    The difference in stratum size and stratum variability can be optimally allocated using the following formula for determining the sample size from different strata


    ${n_i = \frac{n.n_i\sigma_i}{n_1\sigma_1+n_2\sigma_2+…+n_k\sigma_k}\ for\ i = 1,2 …k}$

    Where −

    • ${n_i}$ = the sample size of i strata.
    • ${n}$ = the size of strata.
    • ${\sigma_1}$ = the standard deviation of i strata.

    In addition to it, there might be a situation where cost of collecting a sample might be more in one strata than in other. The optimal disproportionate sampling should be done in a manner that

    ${\frac{n_1}{n_1\sigma_1\sqrt{c_1}} = \frac{n_2}{n_2\sigma_1\sqrt{c_2}} = … = \frac{n_k}{n_k\sigma_k\sqrt{c_k}}}$

    Where ${c_1, c_2, … ,c_k}$ refer to the cost of sampling in k strata. The sample size from different strata can be determined using the following formula:

    ${n_i = \frac{\frac{n.n_i\sigma_i}{\sqrt{c_i}}}{\frac{n_1\sigma_1}{\sqrt{c_i}}+\frac{n_2\sigma_2}{\sqrt{c_2}}+…+\frac{n_k\sigma_k}{\sqrt{c_k}}}\ for\ i = 1,2 …k}$


Problem Statement:

An organisation has 5000 employees who have been stratified into three levels.

  • Stratum A: 50 executives with standard deviation = 9
  • Stratum B: 1250 non-manual workers with standard deviation = 4
  • Stratum C: 3700 manual workers with standard deviation = 1

How will a sample of 300 employees are drawn on a disproportionate basis having optimum allocation?


Using the formula of disproportionate sampling for optimum allocation.

${n_i = \frac{n.n_i\sigma_i}{n_1\sigma_1+n_2\sigma_2+n_3\sigma_3}} \\[7pt]
\, For Stream A, {n_1 = \frac{300(50)(9)}{(50)(9)+(1250)(4)+(3700)(1)}} \\[7pt]
\, = {\frac{135000}{1950} = {14.75}\ or\ say\ {15}} \\[7pt]
\, For Stream B, {n_1 = \frac{300(1250)(4)}{(50)(9)+(1250)(4)+(3700)(1)}} \\[7pt]
\, = {\frac{150000}{1950} = {163.93}\ or\ say\ {167}} \\[7pt]
\, For Stream C, {n_1 = \frac{300(3700)(1)}{(50)(9)+(1250)(4)+(3700)(1)}} \\[7pt]
\, = {\frac{110000}{1950} = {121.3}\ or\ say\ {121}}$

Table of Contents
1.statistics adjusted rsquared

2.statistics analysis of variance

3.statistics arithmetic mean

4.statistics arithmetic median

5.statistics arithmetic mode

6.statistics arithmetic range

7.statistics bar graph

8.statistics best point estimation

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10.statistics binomial distribution

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12.statistics boxplots

13.statistics central limit theorem

14.statistics chebyshevs theorem

15.statistics chisquared distribution

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18.statistics cluster sampling

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20.statistics combination

21.statistics combination with replacement

22.statistics comparing plots

23.statistics continuous uniform distribution

24.statistics cumulative frequency

25.statistics coefficient of variation

26.statistics correlation coefficient

27.statistics cumulative plots

28.statistics cumulative poisson distribution

29.statistics data collection

30.statistics data collection questionaire designing

31.statistics data collection observation

32.statistics data collection case study method

33.statistics data patterns

34.statistics deciles statistics

35.statistics dot plot

36.statistics exponential distribution

37.statistics f distribution

38.statistics f test table

39.statistics factorial

40.statistics frequency distribution

41.statistics gamma distribution

42.statistics geometric mean

43.statistics geometric probability distribution

44.statistics goodness of fit

45.statistics grand mean

46.statistics gumbel distribution

47.statistics harmonic mean

48.statistics harmonic number

49.statistics harmonic resonance frequency

50.statistics histograms

51.statistics hypergeometric distribution

52.statistics hypothesis testing

53.statistics interval estimation

54.statistics inverse gamma distribution

55.statistics kolmogorov smirnov test

56.statistics kurtosis

57.statistics laplace distribution

58.statistics linear regression

59.statistics log gamma distribution

60.statistics logistic regression

61.statistics mcnemar test

62.statistics mean deviation

63.statistics means difference

64.statistics multinomial distribution

65.statistics negative binomial distribution

66.statistics normal distribution

67.statistics odd and even permutation

68.statistics one proportion z test

69.statistics outlier function

70.statistics permutation

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73.statistics poisson distribution

74.statistics pooled variance r

75.statistics power calculator

76.statistics probability

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78.statistics probability multiplicative theorem

79.statistics probability bayes theorem

80.statistics probability density function

81.statistics process capability cp amp process performance pp

82.statistics process sigma

83.statistics quadratic regression equation

84.statistics qualitative data vs quantitative data

85.statistics quartile deviation

86.statistics range rule of thumb

87.statistics rayleigh distribution

88.statistics regression intercept confidence interval

89.statistics relative standard deviation

90.statistics reliability coefficient

91.statistics required sample size

92.statistics residual analysis

93.statistics residual sum of squares

94.statistics root mean square

95.statistics sample planning

96.statistics sampling methods

97.statistics scatterplots

98.statistics shannon wiener diversity index

99.statistics signal to noise ratio

100.statistics simple random sampling

101.statistics skewness

102.statistics standard deviation

103.statistics standard error se

104.statistics standard normal table

105.statistics statistical significance

106.statistics formulas

107.statistics notations

108.statistics stem and leaf plot

109.statistics stratified sampling

110.statistics student t test

111.statistics sum of square

112.statistics tdistribution table

113.statistics ti 83 exponential regression

114.statistics transformations

115.statistics trimmed mean

116.statistics type i amp ii errors

117.statistics variance

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119.statistics weak law of large numbers

120.statistics z table

121.discuss statistics

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