**OUTLINES OF TESTS**

Statistics (Elective) OUTLINES OF TESTS Paper-A 75 marks Paper-B 75 marks Paper-C (Practical) 50 marks Total 200 marks Syllabi and Courses of Reading Paper- A Candidates are required to attempt at least two questions from each Section. Section- I. Descriptive Statistics: (Weight 2/10) Descriptive and inferential Statistics. Population and samples.

Paper-A | 75 marks |

Paper-B |
75 marks |

Paper-C (Practical) |
50 marks |

Total |
200 marks |

#### Syllabi and Courses of Reading

__ ____Paper- A__

*Candidates are required to attempt at least two questions from each Section.*

__Section- I.__

** Descriptive Statistics:** (Weight 2/10)

Descriptive and inferential Statistics. Population and sample. Variables. Measurement scales. Sources of Statistical data in Pakistan. Description of data by frequency tables and graphs. Stem and leaf plots and Box and whisker plots. Measures of Central Tendency. Measures of location: A.M., H.M., G.M., Mode, Median, Quartiles. Properties of Mean with proofs. Weighted Arithmetic mean. Empirical Relation between Mean, Median and Mode. Relative Merits and Demerits of various averages. Measures of dispersion: Absolute and Relative Measures, Range, Semi-Inter Quartile Range, Mean Deviation, Variance, Standard Deviation. Coefficient of Variation. Coefficient of Mean Deviation. Coefficient of Quartile Deviation. Properties of Variance and Standard Deviation with proofs. Standardized Variables. Description both for population and sample and their properties. Chebychev’s Theorem and its application. Moments, Moments Ratios, Sheppard’s Correction, Skewness and Kurtosis.

**(Weight 1/10)**

__Method of Least Squares:__Scatter diagram. Principle of least squares. Deduction and solution of normal equations of general linear model. Curve fitting. Equations of approximating curves by the method of least squares up to third degree polynomials. Fitting of exponential of the type (1) y= ae

^{bx}(2) y= ab

^{x}(3) y= ax

^{b. }Graphic representation of the curves. Interpolation and Extrapolation graphically. Criteria for fitting a suitable curve.

**(Weight 1/10)**

__Time Series:__Time series. Decomposition of Time Series. Measurement of Trend, Seasonal (Additive and multiplicative models), and cyclical variations. Seasonal indices. Deseasonalisation of data.

**(Weight 1/10)**

__Index Numbers:__Index number. Simple and composite indices. Problems in construction of index numbers. Laspayre, Paasche, Marshall-Edgworth, Fisher ideal, Walsh and Palgraves indices. Shifting of base. Quantity index numbers. Theoretical tests for index numbers. Consumer price index. Construction and uses of index numbers in Pakistan. Sensitive Price Indicator.

__Section – II.__

**(Weight 1/10)**

__Concepts of Probability:__Operation in sets. Cartesian product set. Random experiment. Sample space and event. Rules of counting introduction to probability and axioms of probability, emphasizing to concepts, facts, interpretation and illustrating examples. Basic laws of probability, Conditional and marginal probabilities. Independence of events. Baye’s theorem and its application. (Proof not required).

__Random Variable: (Discrete)__**(Weight:**

*P*

*lease see Note No. 1 below*)

Random Variable, Discrete random variable. Probability function, probability distribution function. Mathematical expectation and its properties. Joint distribution of two discrete random variables. Marginal and conditional distributions. Mean, Variance, moments, covariance and correlation of two discrete random variables. Moment generating function and its properties.

**(Weight:**

__Discrete Probability Distributions:__*Please see Note No. 1 below*)

Uniform, Bernoulli, Multinomial, Hypergeometric, poisson. Negative Binomial and Geometric distributions with their derivations, properties, applications and their fitting to statistical data.

__(Note No. 1__

__For Random variable (Discrete) and Discrete probability Distributions common weight is 2/10)__

__Random Variable: (Continuous)__**(Weight 1/10)**

Continuous random variable. Probability distribution of a continuous random variable. Probability density function and probability distribution function. Joint distribution of two continuous random variables. Marginal and conditional distributions. Mathematical expectation and its properties. Moment generating function. Covariance and correlation of two random variables. Mean, Median, Mode, Geometric mean, Harmonic mean, Mean deviation. Variance and moments of simple continuous functions.

**(Weight 1/10)**

__Continuous Probability Distributions:__Uniform, Exponential and Normal distributions with derivations. Their properties, applications and fitting of statistical data. Normal approximation to the Binomial and Poisson distributions (just applications)