Class 11 Economics — Statistics for Economics
Measures of Central Tendency: Arithmetic Mean
Complete Study + Revision Pack
Easy explanation • Formula sheet • Solved numericals • NCERT-style important questions • Common
mistakes • 20-question practice test • One-page last-minute revision
1. Easy Explanation
Central tendency means finding one value that represents the whole group of data. The three common
measures are Arithmetic Mean (Mean), Median and Mode.
Arithmetic Mean is what we usually call the average. We add all observations and divide by the number of
observations. It uses every value in the data, so even one very large or very small value can affect it.
2. Key Terms
Term Meaning
Observation A value/item in the data set.
N Number of observations (for an individual series).
f Frequency — number of times a value occurs.
Σ Sigma; means “sum of”. ΣX means sum of all X values.
X■ Arithmetic Mean of X.
3. All Important Formulas
Individual series — Direct method: X■ = ΣX / N
Discrete/continuous frequency series — Direct method: X■ = ΣfX / Σf
Assumed mean method: X■ = A + Σfd / Σf, where d = X − A
Step-deviation method: X■ = A + (Σfu / Σf) × h, where u = (X − A)/h
Combined mean: X■ = (n■X■■ + n■X■■ + ... + n■X■■) / (n■+n■+...+n■)
Weighted mean: X■w = ΣWX / ΣW
4. Solved Numerical Examples
Example 1 — Individual series
Find the mean of 4, 6, 8, 10, 12.
ΣX = 4+6+8+10+12 = 40; N = 5.
X■ = 40/5 = 8.
Example 2 — Discrete frequency series
X f fX
10 2 20
20 3 60
30 4 120
40 1 40
, Total 10 240
X■ = ΣfX / Σf = 240/10 = 24.
Example 3 — Assumed mean method
Suppose A = 30 and X values are 10, 20, 30, 40, 50 with frequencies 1, 2, 3, 2, 1. Calculate d = X−A, then fd. Σf
= 9 and Σfd = 0. Therefore X■ = 30 + 0/9 = 30.
Example 4 — Combined mean
Group 1: n■=20, mean=60. Group 2: n■=30, mean=70.
Combined mean = (20×60 + 30×70)/(20+30) = 3300/50 = 66.
Measures of Central Tendency: Arithmetic Mean
Complete Study + Revision Pack
Easy explanation • Formula sheet • Solved numericals • NCERT-style important questions • Common
mistakes • 20-question practice test • One-page last-minute revision
1. Easy Explanation
Central tendency means finding one value that represents the whole group of data. The three common
measures are Arithmetic Mean (Mean), Median and Mode.
Arithmetic Mean is what we usually call the average. We add all observations and divide by the number of
observations. It uses every value in the data, so even one very large or very small value can affect it.
2. Key Terms
Term Meaning
Observation A value/item in the data set.
N Number of observations (for an individual series).
f Frequency — number of times a value occurs.
Σ Sigma; means “sum of”. ΣX means sum of all X values.
X■ Arithmetic Mean of X.
3. All Important Formulas
Individual series — Direct method: X■ = ΣX / N
Discrete/continuous frequency series — Direct method: X■ = ΣfX / Σf
Assumed mean method: X■ = A + Σfd / Σf, where d = X − A
Step-deviation method: X■ = A + (Σfu / Σf) × h, where u = (X − A)/h
Combined mean: X■ = (n■X■■ + n■X■■ + ... + n■X■■) / (n■+n■+...+n■)
Weighted mean: X■w = ΣWX / ΣW
4. Solved Numerical Examples
Example 1 — Individual series
Find the mean of 4, 6, 8, 10, 12.
ΣX = 4+6+8+10+12 = 40; N = 5.
X■ = 40/5 = 8.
Example 2 — Discrete frequency series
X f fX
10 2 20
20 3 60
30 4 120
40 1 40
, Total 10 240
X■ = ΣfX / Σf = 240/10 = 24.
Example 3 — Assumed mean method
Suppose A = 30 and X values are 10, 20, 30, 40, 50 with frequencies 1, 2, 3, 2, 1. Calculate d = X−A, then fd. Σf
= 9 and Σfd = 0. Therefore X■ = 30 + 0/9 = 30.
Example 4 — Combined mean
Group 1: n■=20, mean=60. Group 2: n■=30, mean=70.
Combined mean = (20×60 + 30×70)/(20+30) = 3300/50 = 66.
