them comprehensible. It facilitates data processing. A number of statistical | Class 12 Geography Notes
By ConceptScroll Team · Published on 17 July 2026 · 4 min read
them comprehensible. It facilitates data processing. A number of statistical – this guide gives you a concise, exam-ready overview of them comprehensible. It facilitates data processing. A number of statistical from Class 12 Geography, written by ConceptScroll editors and reviewed against the latest NCERT textbook.
Comparison of Mean, Median and Mode
Mean, median, and mode are three fundamental measures of central tendency that can be compared using the normal distribution curve, also known as the bell-shaped curve. This curve is symmetrical, with most observations clustering around the central value. In a perfectly normal distribution, the mean, median, and mode coincide at the same point, representing the highest frequency score. This symmetry implies that half the observations lie above and half below this central value.
Many human traits such as intelligence, personality scores, and student achievements follow normal distributions. However, when data is skewed, these measures do not coincide. In positively skewed distributions, the mean is greater than the median, which is greater than the mode. Conversely, in negatively skewed distributions, the mean is less than the median, which is less than the mode. Understanding these relationships helps in selecting the appropriate measure of central tendency based on data characteristics. The chapter includes diagrams illustrating normal, positive skew, and negative skew distributions to visualize these concepts.
📊 Diagram: Fig. 2.1 depicts a normal distribution curve with mean, median, and mode coinciding at the center (score 100). Fig. 2.2 shows a positively skewed distribution with mean shifted right. Fig. 2.3 shows a negatively skewed distribution with mean shifted left.
🔗 Connection: This section concludes the theoretical part and leads to exercises and activities for practice.
Frequently asked questions
1. Choose the correct answer from the four alternatives given below: (i) The measure of central tendency that does not get affected by extreme values: (a) Mean (b) Mean and Mode (c) Mode (d) Median (ii) The measure of central tendency always coinciding with the hump of any distribution is: (a) Median (b) Median and Mode (c) Mean (d) Mode
(i) The measure of central tendency that does not get affected by extreme values is the Median (d). Mean is affected by extreme values, Mode is not necessarily unaffected. Median is resistant to extreme values.
(ii) The measure of central tendency always coinciding with the hump of any distribution is the Mode (d). The Mode is the value that appears most frequently and corresponds to the peak (hump) of the distribution.
2. Answer the following questions in about 30 words: (i) Define the mean. (ii) What are the advantages of using mode?
(i) Mean is the sum of all observations divided by the number of observations. It represents the average value of the data set.
(ii) Advantages of mode:
- It is easy to understand and calculate.
- It can be used for qualitative data.
- It represents the most common value in the data set.
- It is not affected by extreme values.
3. Answer the following questions in about 125 words: (i) Explain relative positions of mean, median and mode in a normal distribution and skewed distribution with the help of diagrams. (ii) Comment on the applicability of mean, median and mode (hint: from their merits and demerits).
(i) In a normal distribution, mean = median = mode, all three measures coincide at the center of the symmetric bell-shaped curve.
In a positively skewed distribution, mode < median < mean. The tail is stretched to the right, so mean is pulled towards higher values.
In a negatively skewed distribution, mean < median < mode. The tail is stretched to the left, so mean is pulled towards lower values.
Diagrams typically show the bell curve for normal distribution and skewed curves with shifted pea
Activity 1. Take an imaginary example applicable to geographical analysis and explain direct and indirect methods of calculating mean from ungrouped data.
Direct Method: Suppose the data set of ungrouped data is: 5, 7, 9, 10, 12. Mean = (5 + 7 + 9 + 10 + 12) / 5 = 43 / 5 = 8.6
Indirect Method: Choose an assumed mean (A), say 9. Calculate deviations d = x - A: (-4, -2, 0, 1, 3) Sum of deviations Σd = (-4) + (-2) + 0 + 1 + 3 = -2 Mean = A + (Σd / n) = 9 + (-2/5) = 9 - 0.4 = 8.6
Both methods yield the same mean value.
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- computer hardware and the application software are referred as the Database | Class 12 Geography Notes
Clear NCERT-aligned notes on computer hardware and the application software are referred as the Database for Class 12 Geography.
- computer hardware and the application software are referred as the Database | Class 12 Geography Notes
Clear NCERT-aligned notes on computer hardware and the application software are referred as the Database for Class 12 Geography.
- computer hardware and the application software are referred as the Database | Class 12 Geography Notes
Clear NCERT-aligned notes on computer hardware and the application software are referred as the Database for Class 12 Geography.