Statistics – Formula & Equation Sheet
Essential formulas and equations from Mathematic, tailored for Class 10 in Mathematics.
This one-pager compiles key formulas and equations from the Statistics chapter of Mathematic. 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
Mean (Grouped Data): x = Σ(fi xi) / Σfi
x is the mean, fi is the frequency of the ith class, and xi is the class mark. This formula calculates the average of a grouped dataset.
Class Mark: xi = (Lower Limit + Upper Limit) / 2
xi represents the midpoint of a class interval. It serves as a representative value for calculations.
Cumulative Frequency: CF = Σfi
CF is the cumulative frequency, which represents the total number of observations up to the ith class. It is essential for constructing ogives.
Assumed Mean Method: x = a + (Σfi di / Σfi)
a is the assumed mean, di is the difference between class marks and assumed mean. This method simplifies calculations for the mean.
Step-Deviation Method: x = a + h(u)
u = (Σfi ui) / Σfi, where ui is the standardized deviation. h is the class width, and this method also streamlines mean calculations.
Modal Class: Mode = L + (f1 - f0) / (2f1 - f0 - f2) × h
L is the lower boundary of the modal class, f1 is the frequency of the modal class, f0 is the frequency of the class before it, and f2 is the frequency of the class after it. This formula finds the mode of grouped data.
Variance (Grouped Data): σ² = Σfi (xi - x)² / N
σ² is the variance, with fi as the frequency, xi as class marks, x as the mean, and N being the total frequency. It measures the dispersion of the dataset.
Standard Deviation: σ = √(σ²)
σ represents the standard deviation, a measure of how spread out the values are in a dataset.
Cumulative Frequency for Ogives: CF = Σfi from lowest class to ith class
This calculation helps to ascertain the cumulative distribution of values, useful for graphical representation as ogives.
Relative Frequency: rf = fi / N
rf is the relative frequency of the ith class. It indicates the proportion of the total dataset that falls within that class.
Equations
Mean of Deviations: d = Σfi di / Σfi
d is the mean of deviations, which offers a different method to calculate mean by summarizing the deviations.
Cumulative Frequency for Ogive: CF = fi + CF(i-1)
CF is found by adding the frequency of the current class to the cumulative frequency of the previous class.
Standard Deviation Formula: σ = √(Σfi (xi - x)² / N)
This formula calculates the spread of values in a dataset by assessing the average deviation from the mean.
Total Frequency: N = Σfi
N is the total number of observations in a dataset, calculated by summing all class frequencies.
Difference of Two Means: d = x1 - x2
This equation finds the difference between two means which can show relative performance across groups.
Mean from Frequencies: x = Σxi fi / Σfi
This summarizes the calculation of mean where x is averaged over all values weighted by their frequencies.
Weighted Mean: x̄ = Σwi xi / Σwi
Here, wi represents weights assigned to each observation. It determines an average that accounts for varying importance.
Finding Mode: Mode = L + (f1 - f0) / (2f1 - f0 - f2) × h
This calculates the mode by assessing the frequency distribution of the data, particularly in a grouped context.
Probability: P(A) = N(A) / N
P(A) is the probability of event A occurring, where N(A) is the number of favorable outcomes and N is the total number of outcomes.
Z-Score: z = (x - μ) / σ
z represents the Z-score, a measure of how many standard deviations an element is from the mean μ.
