This chapter focuses on measures of central tendency, which are crucial for summarizing data in a meaningful way. It helps to find a typical value that represents a dataset, aiding comparisons and understanding.
Measures of Central Tendency – Formula & Equation Sheet
Essential formulas and equations from Statistics for Economics, tailored for Class 11 in Economics.
This one-pager compiles key formulas and equations from the Measures of Central Tendency chapter of Statistics for Economics. 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
Arithmetic Mean (X̄) = ΣX / N
X̄ represents the arithmetic mean, ΣX is the sum of all observations, and N is the total number of observations. This formula calculates the average of a data set.
Median = (N+1)/2 th item
The median is the middle value in a sorted data set, found by using the position formula where N is the number of observations.
Mode (Mo) = Value with highest frequency
Mode is the value that appears most frequently in a data set. It can be determined by identifying the observation with the maximum frequency.
Weighted Arithmetic Mean = (Σ(Wi × Xi)) / ΣWi
It accounts for varying importance of data points Xi (values) weighted by Wi (weights). Use it when different observations have different significance.
Quartiles: Q1 = (N+1)/4 th item, Q2 = Median, Q3 = 3(N+1)/4 th item
Q1 and Q3 define the first and third quartiles, respectively, splitting data into four equal parts.
Percentiles: Pk = (k(N))/100 th item
Pk represents the k-th percentile in a sorted data set of N observations, indicating the value below which a certain percentage of data falls.
Sum of deviations from Mean = Σ(Xi - X̄) = 0
This property states that the total of all deviations from the arithmetic mean always equals zero.
Median in continuous distribution = L + ((N/2 - cf) / f) × h
Where L is the lower limit of the median class, cf is the cumulative frequency of the class before median class, f is the frequency of median class, and h is the class width.
Step Deviation Method: X̄ = A + (Σfd/N) × c
X̄ is the mean, A is the assumed mean, fd are the deviations multiplied by frequencies, and c is the common factor used to simplify calculations.
Mode in continuous data: Mo = L + ((D1 / (D1 + D2)) × h)
Where L is the lower limit of the modal class, D1 is the frequency of modal class minus the frequency of the class before, and D2 is the frequency of modal class minus the frequency of the class after.
Equations
X̄ = (X1 + X2 + ... + XN) / N
This represents the calculation of arithmetic mean from ungrouped data, summing up all values and dividing by their count.
Position of Median = (N + 1) / 2
Used to determine the index of the median in a sorted dataset. If N is even, average the two central values.
Q1 = value at (N+1)/4 th position
The first quartile Q1 indicates the value below which 25% of the data falls.
Mo (discrete series) = Mode is the value with maximum frequency
Determining the mode in a simple frequency distribution by identifying the highest frequency value.
ΣX = N × X̄
This is the rearrangement of the mean formula, determining total sum from the mean and number of observations.
D = X - X̄
Deviation (D) from the mean is calculated as the individual observation (X) minus the mean (X̄).
P_k = (kN) / 100 th item
This formula allows for the calculation of the k-th percentile of a data set.
L + (N/2 - cf) / f × h
This formula calculates the median in continuous frequency distribution.
Mo = L + (D1 / (D1 + D2)) × h
Calculates mode in continuous data distribution utilizing the differences in frequencies.
X̄ = A + Σfd/N
Mean using step deviation technique, applying the common factor to simplify calculations.
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