Karnataka II PUC Statistics (KSEAB) flashcards

34 cards. Read the term and the definition here. The deck at the top of this page is optional.

Statistics (plural sense)

Numerical facts collected systematically for a definite purpose, presented and analysed to draw conclusions; the figures themselves, such as census counts or price data.

Primary data

Data collected first-hand by the investigator for the specific enquiry at hand, through interviews, questionnaires, schedules or direct observation, before any published use.

Census versus sample method

Census studies every unit of the population and is costlier but free of sampling error; the sample method studies a representative part and is quicker and cheaper.

Non-sampling error

Error in a survey not caused by studying only a part, arising from faulty frames, non-response, ambiguous questions, measurement mistakes or recording and processing errors.

Exclusive class intervals

Grouped classes in which the upper limit is excluded, such as 10–20 and 20–30; an observation equal to 20 falls in the second class, not the first.

Class mark

The mid-point of a class interval, computed as (lower limit + upper limit)/2; it represents the class in computing grouped mean and standard deviation.

Ogive

A cumulative frequency curve, drawn as 'less than' or 'more than' type, used to locate the median, quartiles, deciles and percentiles graphically.

Pie chart angle

For a component with frequency f out of total N, the sector angle is (f/N) × 360 degrees; all sectors together complete a full circle.

Combined arithmetic mean

The mean of two or more groups pooled together, given by (n1 x̄1 + n2 x̄2)/(n1 + n2); it weights each group mean by its size.

Median of grouped data

L + [(N/2 − cf)/f] × h, where L is the lower limit of the median class, cf the cumulative frequency before it, f its frequency and h its width.

Empirical mode formula

For moderately skewed data, Mode = 3 Median − 2 Mean; it approximates the mode when the distribution is not badly skewed.

Geometric mean

The nth root of the product of n positive observations, computed as antilog(Σ log x / n); appropriate for averaging ratios and growth rates.

Coefficient of variation

CV = (standard deviation / mean) × 100; a unit-free relative measure used to compare consistency of two series, with a smaller CV meaning greater consistency.

Quartile deviation

QD = (Q3 − Q1)/2, half the interquartile range; with coefficient (Q3 − Q1)/(Q3 + Q1), it ignores the extreme quarter values.

Short-cut variance formula

σ² = (Σfx²/N) − (Σfx/N)² for grouped data using class marks x; subtracting the squared mean from the mean of squares.

Mean deviation minimum property

Mean deviation Σ|x − A|/n is least when deviations are taken about the median; about the mean it is not minimal.

Karl Pearson's skewness

SK = (Mean − Mode)/σ, or 3(Mean − Median)/σ when the mode is ill-defined; positive means right-skewed, negative means left-skewed, zero means symmetric.

Leptokurtic distribution

A distribution with β2 = μ4/μ2² greater than 3 (γ2 > 0); it has a sharper peak and heavier tails than the normal curve.

Mesokurtic distribution

A distribution with β2 equal to 3, so γ2 = 0; the normal curve is the standard mesokurtic reference distribution.

Spearman's rank correlation

ρ = 1 − 6Σd²/[n(n² − 1)], where d is the difference between ranks of paired observations; used when data are ordinal or ranks.

Regression coefficients product

For two variables, b_yx × b_xy = r², the square of the correlation coefficient; both regression lines pass through the point (x̄, ȳ).

Lines of regression

Two lines, y on x for predicting y and x on y for predicting x; they coincide when r = ±1 and are perpendicular when r = 0.

Fisher's ideal index

The geometric mean of the Laspeyres and Paasche indices, √(L × P); it satisfies both the time-reversal and factor-reversal tests.

Paasche price index

(Σp1q1 / Σp0q1) × 100, using current-year quantities as weights; it tends to understate price rise compared with the Laspeyres index.

Cost of living index

Σ(p1/p0)w / Σw × 100, where w are base-period consumption weights of items in a family's basket; it measures change in real living cost.

Time series components

Secular trend (long-term direction), seasonal variation (within-year pattern), cyclical variation (multi-year swings) and irregular variation (random shocks).

Centred moving average

For an even period such as 4, a two-period average of successive moving averages, used to align the trend value exactly with the original time point.

Least squares trend

Fitting Y = a + bX by minimising Σ(Y − a − bX)²; with X coded so ΣX = 0, a = ΣY/N and b = ΣXY/ΣX².

Conditional probability

P(A|B) = P(A ∩ B)/P(B), the probability of A given that B has occurred; defined only when P(B) is greater than zero.

Independent events

Two events A and B are independent when P(A ∩ B) = P(A)P(B), equivalently P(A|B) = P(A); occurrence of one gives no information about the other.

Binomial distribution mean

For n independent trials with success probability p, the mean is np, variance npq and standard deviation √(npq), with q = 1 − p.

Normal curve inflection points

Points at x = μ ± σ where the curve changes concavity; the total area under the curve is 1 and the distribution is symmetric about μ.

Finite population correction

The factor (N − n)/(N − 1) applied to the variance of the sample mean when sampling without replacement from a finite population; it is near 1 for large N.

Central limit theorem

For large sample size n, the sampling distribution of the sample mean is approximately normal with mean μ and standard error σ/√n, whatever the population shape.