Statistics Test (CA - CPT)

Standard deviation is indeed an absolute measure of dispersion because it is expressed in the same units as the original data. Unlike relative measures like coefficient of variation, standard deviation gives the actual spread of data points around the mean in concrete units.

A platykurtic distribution has less concentration of values around the center compared to a normal distribution, resulting in a flatter curve with thinner tails. This matches the description given in the statement.

Standard deviations of multiple component parts can be combined using the variance addition rule. For independent parts, variances add directly, and the combined standard deviation is the square root of the sum of variances.

When the coefficient of kurtosis (γ₂) equals zero, the distribution is mesokurtic, which resembles a normal distribution. A leptokurtic curve occurs when γ₂ > 0, indicating more concentration around the mean with heavier tails.

Kurtosis is calculated as the ratio of the fourth moment about the mean to the square of the variance (second moment). This formula uses both the fourth and second central moments, making the statement true.

Symmetry (zero skewness) does not determine kurtosis. A distribution can be perfectly symmetrical yet be leptokurtic (sharper peak) or platykurtic (flatter) than normal. Kurtosis measures tail heaviness and peak concentration independently of symmetry.

Bowley's coefficient of skewness is based on quartiles (Q1, Q2, Q3), not being any 'fourth measure'. There are various measures of skewness (Pearson's, moment-based, Bowley's), but Bowley's quartile-based coefficient isn't designated as a fourth specific measure.

Spearman's rank correlation method converts actual numerical data into ranks before calculating correlation. This means it works perfectly fine when actual data is given - the data is simply transformed to ranks first.

A linear relationship between two variables means their graph forms a straight line. This is the fundamental definition - when y = a + bx (or similar forms), plotting x vs y gives a straight line.

A scatter diagram visually displays the relationship between two variables but does not provide a numerical value for the correlation coefficient. To measure the actual correlation coefficient value, you need to use calculation methods like Pearson's or Spearman's formulas.

In common language, 'association' vaguely suggests connection, but in statistics it specifically measures the strength and direction of relationship between variables. Statistical association is more precise and quantifiable than casual linguistic usage.

Karl Pearson's correlation coefficient IS unduly influenced by extreme items because it uses the mean, which is sensitive to outliers. Extreme values can significantly distort the correlation value, making this statement false.

Rank correlation methods like Spearman's coefficient can handle tied ranks using appropriate formulas that adjust for the tied positions. The method remains valid when equal ranks are assigned.

For n attributes, each attribute can be present or absent, giving 2^n total class frequencies (the number of cells in a 2×2×...×2 contingency table), not 3^n. The formula 3^n would apply if each attribute had three states instead of two.

All class frequencies (marginal and cell frequencies) can indeed be expressed as sums of ultimate class frequencies (the smallest cell frequencies in a multi-way contingency table). This is a fundamental property of categorical data analysis.

The proportion method only reveals whether association exists (nature) by comparing observed proportions to expected values. To measure the degree (strength) of association, you need coefficients like Yule's Q or the coefficient of association.

Index numbers are indeed called barometers of economic activity because they measure changes in economic variables like prices, production, and employment over time, providing a snapshot of economic health.

The condition (AB)(αβ) = (Aβ)(αB) is the mathematical test for independence between attributes A and B. If this equality is NOT satisfied, the attributes are associated. When the product of opposite diagonal frequencies equals the product of the other diagonal, attributes are independent (not associated).

Weighted average of relatives (like price relatives) from different items or groups can be combined mathematically to form composite indices. This is how aggregate price indices are constructed from individual component indices.

Unweighted indices implicitly assign equal weights to all items, which is itself a weighting scheme. When no explicit weights are given, the assumption of equal importance means weights are implicitly equal to 1 for all items.

Fisher's ideal index satisfies both the time reversal test and factor reversal test, making it 'ideal'. The time reversal test requires that Pt_0 × P0_t = 1, which Fisher's index meets by construction.

The circular test requires that an index number should work consistently when chained over multiple periods (P1_2 × P2_3 × P3_1 = 1). Laspeyer's method uses base-period quantities as weights and does NOT satisfy this test, while Fisher's ideal index does.

A larger sample size reduces sampling error and better captures the population diversity, making it more representative of the population characteristics. This is why larger samples generally provide more reliable estimates.

Judgment sampling relies on expert knowledge and convenience, not random selection. It's a non-probability sampling method because each element does not have a known, non-zero probability of selection. Probability sampling requires random mechanisms.

In statistics, a homogeneous universe means all elements have similar characteristics with minimal variation. When variation is low, a smaller sample can adequately represent the entire universe because there's less diversity to capture. This reduces the required sample size while maintaining statistical validity.