Data Processing Class 12 NCERT Solutions PDF 2026-27

Ans. There are 3 end-of-chapter exercise questions in NCERT Class 12 Geography Chapter 2 Data Processing. Question 1 has 2 MCQ sub-parts, Question 2 has 2 short-answer sub-parts (about 30 words each), and Question 3 has 2 long-answer sub-parts (about 125 words each). All questions are solved with full plain-English working and Expert Solutions in our data processing class 12 ncert solutions PDF.

Ans. All three are measures of central tendency, meaning they give a single representative value for a dataset. The mean is the arithmetic average: sum of all values divided by the count. It uses every observation but is sensitive to extreme values. The median is the middle value of an ordered dataset; it is positional and not affected by outliers. The mode is the value that occurs most often; it always sits at the peak (hump) of the frequency curve and is the only measure that works on categorical data. The NCERT chapter covers direct and indirect methods of computing the mean for both ungrouped and grouped data.

Ans. In a normal (symmetric bell-shaped) distribution, Mean = Median = Mode. All three coincide at the centre of the curve. In a positively skewed distribution (long tail to the right), the order is Mode less than Median less than Mean, with the mean pulled furthest toward the long tail. In a negatively skewed distribution (long tail to the left), the order reverses: Mean less than Median less than Mode. The empirical relation for moderately skewed distributions is Mode = 3 Median - 2 Mean. In a CBSE board answer for Q3(i), always draw all three curves and label the averages on each for full marks.

Ans. The mode has five practical advantages in geography: (1) it is the easiest average to locate - just find the value with the highest frequency; (2) it is not affected by extreme values, so one unusually high rainfall year does not distort it; (3) it is the only average that works on categorical data, for example "most common crop in a district" or "most frequent wind direction" - questions that mean and median cannot answer; (4) it sits exactly at the histogram peak, making it the most intuitive average for visual data; and (5) it can be used even when end-class limits are open and the mean cannot be computed. These five advantages are the expected answer to NCERT Q2(ii).

Ans. For grouped data, use the interpolation formula: M = l + (i/f)(N/2 - c), where M is the median, l is the lower limit of the median class, i is the class interval, f is the frequency of the median class, N is the total number of observations, and c is the cumulative frequency of the class before the median class. To identify the median class: compute N/2, then scan the cumulative frequency column and find the first class whose cumulative frequency exceeds N/2. Always write the identified median class explicitly in your answer before substituting into the formula, as CBSE markers award a separate step mark for this.

Ans. The empirical relation is: Mode = 3 Median - 2 Mean. This relation holds approximately for moderately skewed distributions. It means if you know any two of the three averages, you can estimate the third. For example, if Mean = 50 and Median = 45, then Mode = (3 x 45) - (2 x 50) = 135 - 100 = 35. This relation is directly implied by the positions of the three averages on the frequency curve: in a positively skewed curve, the mean is largest, then median, then mode, and this formula maintains that gap relationship. It appears as a 1-mark or 2-mark question in CBSE board papers for this chapter.

Ans. A normal distribution curve is a bell-shaped, symmetric frequency curve where most observations cluster around the central value and frequency decreases equally on both sides. In a perfect normal distribution, Mean = Median = Mode, all three coincide at the apex. The NCERT chapter (Fig. 2.1) introduces it as a reference shape because many natural phenomena in geography (temperatures across a region, heights across a population) roughly follow this distribution. The chapter then introduces positive skew (Fig. 2.2) and negative skew (Fig. 2.3) as departures from this symmetric ideal, and explains how the three averages separate in each case. Understanding the normal curve is the foundation for answering Q3(i) correctly.

Ans. The indirect (or deviation) method of computing the mean is used when raw values are large and adding them directly is tedious. You choose an assumed mean (A), compute the deviation d = x - A for each observation, find the mean of the deviations, and add it back to A. Formula: Mean = A + (Sum of d / N). The NCERT chapter uses the Malwa Plateau rainfall data with A = 800 mm as an example, giving the same result (926.29 mm) as the direct method. The indirect method is faster for large datasets and is also extended to grouped data using a step-deviation variant with a coding factor. Both the direct and indirect methods must give identical answers, which is the expected verification check in a board exam.

Ans. No major changes to the Practical Work in Geography Part II syllabus for 2026-27. The four-chapter structure (Data: Its Source and Compilation; Data Processing; Graphical Representation of Data; Spatial Information Technology) is unchanged for the current cycle. Chapter 2 Data Processing continues to cover the three measures of central tendency (mean, median, mode) using both ungrouped and grouped data methods. CBSE marking continues to reward formula-then-substitution layout, explicitly labelled median class identification, and diagrams for skewed-distribution questions. Our class 12 geography chapter 2 ncert solutions for 2026-27 are aligned to the unchanged textbook and the latest CBSE sample paper released for the 2026 boards.