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STATISTICS – Formula & Equation Sheet
Essential formulas and equations from Mathematics, tailored for Class 9 in Statistics.
This one-pager compiles key formulas and equations from the STATISTICS chapter of Mathematics. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Key concepts & formulas
Essential formulas, key terms, and important concepts for quick reference and revision.
Formulas
Class-mark = (Upper limit + Lower limit) / 2
Class-mark represents the midpoint of a class interval, used for plotting frequency polygons. It aids in visualizing and interpreting data distributions.
Histogram Area = Width × Height
In a histogram, each rectangle's area corresponds to its frequency. This relationship helps in visualizing how data values are distributed over intervals.
Mean = Σ(f × x) / N
Mean is the average of the dataset. f represents frequency, x represents class-mark, and N is the total number of observations. Essential for measure of central tendency.
Median = {(N + 1)/2}th value
The median is the middle value when data is ordered. For grouped data, it helps locate the central tendency where half the data is above or below it.
Mode = Value with the highest frequency
Mode is the most frequently occurring value in a dataset. In grouped data, it indicates the class interval with maximum frequency.
E = Σf
E represents the total frequency of observations. It is fundamental in summing data points to derive statistical measures.
Relative Frequency = f / N
Relative frequency is the fraction of the total that a particular class represents, aiding in understanding the distribution of data.
Cumulative Frequency = Σf (up to a certain class)
Cumulative frequency totals the frequencies of all classes up to a specific point, useful for identifying medians and quartiles.
Bar Graph Height = Value of Variable
The height of each bar in a bar graph corresponds to the value it represents, providing a clearer comparison of different categories.
Frequency Polygon: Connect midpoints of histogram tops
A frequency polygon visually represents the data's distribution by connecting midpoints of histogram rectangles' tops, used for comparisons.
Equations
Bar Graph: y = f(x)
In a bar graph, the height (y-axis) represents the frequency (f) while the categories (x-axis) represent the variable values.
Histogram Equation: Area = base × height
In histograms, the area under each rectangle (base is the width of the class) represents the corresponding frequency.
Mean for Grouped Data: Mean = Σ(f × x) / Σf
This equation calculates the mean from frequency distributions, where Σ(f × x) sums the product of class frequencies and their midpoints.
Median Class = Ceil[(N/2)]
This identifies the class interval where the median lies in a cumulative frequency distribution.
Mode Class = L + [(f1 - f0) / (2f1 - f0 - f2)] × h
This formula estimates the mode of a grouped frequency distribution. L is the lower boundary of the modal class, h is the class width, and f's represent frequencies.
N = Σf
N represents the total number of observations in a frequency distribution, calculated by summing all frequencies (Σf).
Cumulative Frequency: CF = CF of previous + current frequency
This defines how to calculate the cumulative frequency for each class in a distribution.
Relative Frequency: RF = f/N
This calculates the relative frequency by dividing the frequency of a particular class (f) by the total number of observations (N).
Percentage Frequency = (f/N) × 100
This calculates the percentage frequency to express the frequency of each class as a percentage of the total observations.
Grouped Mean: x̄ = ΣfX / Σf
This formula calculates the mean for grouped data using the frequency and midpoint of each class (X), essential for statistical analysis.
