Some key points to remember

• Descriptive statistics: Deals with summarization of data.
• Inferential statistics: Deals with analysis and interpretation  of data.
• Qualitative variable: Nominal scale
• Ranking: Ordinal scale
• Quantitative variable: Interval scale.
• Qualitative variables are also called as
• Quantitative variables are also called as
• For sake of uniformity, we may designate median as Q₂.
• Coefficient of variation (CV) = SD/mean x 100
• CV measures relative dispersion.
• Mean: Best measure of central tendency
• SD: Best measure of dispersion.
• Skewness: Denotes absence of symmetry

i) +ve when curve has longer tail on left . M₀ < M_d < x̄

ii) -ve when curve has longer tail on right M₀ < M_d < M₀

• Karl Pearson’s skewness : [ -3 ≤ S_k ≤ 3]
• Relation between Q_d, M_d and SD : 6QD = 5Md = 4SD
• Z-test is done when population SD is known and sample size is large.
• X² distribution : To test whether the observed value are in agreement with those which would occur is some specific hypothesis were true.
• The value of correlation ® ranges from -1 to +1.
• Regression : b_yx. b_xy = r²
• Both regression coefficient has same sign.
• CRD is appropriate only when the experimental units are homogenous.
• The formula for GM on n values x₁, x₂ , ….., x_n is ( x₁, x₂ , ….., x_n) ^1/n
• Theory of statistics : Fisher
• 1^st step in summarizing the data is classification.
• Student’s t-test was discovered by W.S Gosset.
• Latin square design is suitable for comparing 5-12 treatments.
• Mean deviation (Md) < Standard deviation (SD).
• Regression coefficient lies between 0 to ∞.
• Correlation coefficient lies between -1 to + 1.
• Value of X² lies between 0 to ∞.
• Mode = 3 median – 2 mean.
• Second moment about mean = Σ( x-x)²/ N
• Rank correlation (R ) = 1-6Σ D²/ N² (N²-1)
• Β₂ – 3 = y₂
• Limit of population correlation = γ ± PE
• Attributes A and B are positive associated if (AB) < (A) x (B) / N
• Coefficient of contingency ( C) = ²/ (N + X²)
• Time interval test is satisfied when P₀₁ x P₁₀ < 1.
• In life table q_x = d_x/ t_x
• If an event can’t take place, probability will be zero.
• PxQ would always be 1.
• Mutually exclusive event P(A) + P(B).
• Independent event P(A) x P(B).
• A and B dependent and B given then, P(B/A) = P(A) / P(A)
• A and B dependent and A given , then P(A/B) = P(AB) / P(B)
• SD of binomial distribution =
• 4^th moment of poisson distribution is m + m².
• SD of poisson distribution is 3m.
• Large sample theory is applicable when N is > 30.
• Difference between 2 means in case of small sample (t) = x̄₁ – x̄₂/ s ₁n₂/ (n₁ + n₂)
• Coefficient of contingency = ²/ N + X³
• X² test = Σ(O-E)/E
• X² test is used to test agreement between observed frequencies and expected frequencies.
• T-test is used when sample size is < 30 and used to test significance of correlation coefficient.
• AM> HM> GM
• Analysis of variance (ANOVA) is used to compare means of more than 2 population.
• Latin square design à comparing 5-12 treatments.
• QD = 0.6745 of SD.
• Classification is 1^st step of tabulation.
• If mean =25 , mode =24 then median = 24.67.
• IN symmetrical distribution, Mean = Median = Mode
• HM = 1/AM [ GM² = AM x HM]
• When the relationship is of quantitative, Correlation is done.
• If A xB/N = AB , attributes are independent.
• X² depends on degree of freedom
• RBD = 2 to 24 treatments.
• Real giant in development of theory of statistics is Fischer.
• Precision of a random sample increases with increase in sample size.s
• Moderate asymmetrical distribution AM > GM> HM
• Unstable average = mode
• Qualitative data = median
• GM =
• Quartile deviation (QD) = Q₃-Q₁ / 2
• Coefficient of QD = Q₃-Q₁ / Q₃+ Q₁
• Measure of variation least affected by extreme observation is mean deviation
• Coefficient of skewness is zero = Symmetrical.
• Coefficient of determination is defined as r².
• If coefficient of skewness is -ve = Q₃ + Q₁ = 2Q
• Regression lines cut each other at the point of X and Y.
• The further the two regression lines cut other, The lesser will be the degree of correlation.
• Attribute A and B are said to be positively associated if AB < A x B/N
• Yule’s coefficient of association can be between +1.
• Laspeyre’s index is based on current year quantities.
• Most of the development in field of stat. à
• P x Q will always be 1.
• The 4^th moment of poisson distribution = m+ m²
• X² test was devised by Karl Pearson

Note:

a) Binomial distribution : James Bernoulli ( French scientist)

b) Poission distribution : Simeon Denis Poisson