NCERT Solutions for Class 12 Geography Practical Work in Geography II Chapter 2: Data Processing

Chapter at a glance

Measure	Key point
Central tendency	A single value representing the whole data set — mean, median, mode
Mean	Sum of values ÷ number of values; direct method ; indirect (assumed mean) method ; affected by extreme values
Median	Middle value of data arranged in order; position (N+1)/2; not affected by extreme values
Mode	Value that occurs most frequently; the hump (peak) of the distribution; may be uni-, bi- or multi-modal
Normal distribution	Symmetrical, bell-shaped; mean = median = mode
Skewed distribution	Positive skew: mode < median < mean; negative skew: mean < median < mode

Exercise Questions

Question 1 (i)

The measure of central tendency that does not get affected by extreme values:
(a) Mean (b) Mean and Mode (c) Mode (d) Median

Answer

The median is the middle value of ordered data, so it is not affected by extreme values. (The mean is affected by extreme values.)

4. Median

Question 1 (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

Answer

The mode is the most frequently occurring value; it always coincides with the peak (hump) of a distribution.

4. Mode

Question 2 (i)

Define the mean.

Answer

The mean (arithmetic average) is the value obtained by dividing the sum of all observations by the number of observations:

It is the most commonly used measure of central tendency.

The mean is the sum of all values divided by the number of values, .

Question 2 (ii)

What are the advantages of using mode?

Answer

1. It is easy to understand and locate — simply the most frequent value; can be found by inspection.
2. It is not affected by extreme values.
3. It can be used for qualitative (nominal) data (e.g. the most common crop, most common type of house).
4. It shows the most typical value — the peak of the distribution — useful in geographical studies (e.g. most common landholding size, modal rainfall).
5. It can be determined graphically.

Mode is easy to understand and find, unaffected by extreme values, usable for qualitative data, shows the most typical value (the peak of the distribution), and can be located graphically.

Question 3 (i)

Explain relative positions of mean, median and mode in a normal distribution and skewed distribution with the help of diagrams.

Answer

Normal distribution: - A symmetrical, bell-shaped curve; most values cluster around the middle and the number of observations decreases symmetrically on both sides. - Mean = median = mode, all at the centre (peak) of the curve. Exactly half the scores lie above and half below the middle.

Positively skewed distribution (skewed to the right): - The tail is longer on the right (a few very high values). - The mode is at the peak, the median lies to its right, and the mean is pulled furthest to the right by the extreme high values: mode < median < mean.

Negatively skewed distribution (skewed to the left): - The tail is longer on the left (a few very low values). - The mean is pulled to the left by low values, the median lies between, and the mode is at the peak on the right: mean < median < mode.

In skewed data, the median often gives a better measure of central tendency than the mean.

In a normal (symmetrical, bell-shaped) distribution, mean = median = mode at the centre. In a positively skewed distribution (long right tail), mode < median < mean; in a negatively skewed distribution (long left tail), mean < median < mode — the mean is pulled towards the tail of extreme values.

Question 3 (ii)

Comment on the applicability of mean, median and mode (hint: from their merits and demerits).

Answer

Conclusion: the choice depends on the nature of data and purpose: mean for symmetrical quantitative data, median for skewed data with extremes, and mode for the most typical or qualitative values.

The mean uses all values and suits further statistics but is distorted by extremes — best for symmetrical data like rainfall or yields. The median is unaffected by extremes and works with open classes but ignores some values — best for skewed data like incomes or landholdings. The mode is simple, works for qualitative data and shows the most typical value but may be ill-defined or multiple — best for the most common item. The choice depends on the data and purpose.

Question Activity – 1

Take an imaginary example applicable to geographical analysis and explain direct and indirect methods of calculating mean from ungrouped data.

Answer

Example: annual rainfall (cm) at 10 stations of a district: 52, 60, 48, 75, 66, 80, 58, 70, 62, 49.

1. Direct method

Q2

Indirect (assumed mean) method — used when values are large or numerous; take an assumed mean A = 60 cm and find deviations d = X − A:

Answer

Station	X (cm)	d = X − 60
1	52	−8
2	60	0
3	48	−12
4	75	+15
5	66	+6
6	80	+20
7	58	−2
8	70	+10
9	62	+2
10	49	−11
		Σd = +20

Both methods give the same mean rainfall of 62 cm; the indirect method simplifies calculation with large numbers.

For rainfall of 52, 60, 48, 75, 66, 80, 58, 70, 62 and 49 cm: direct method ΣX/N = 620/10 = 62 cm; indirect method with assumed mean 60, Σd = 20, so mean = 60 + 20/10 = 62 cm.

Topic checklist

• ☒ Mean, median and mode — definitions and properties (Q 1, 2)
• ☒ Normal and skewed distributions (Q 3 (i))
• ☒ Applicability of measures (Q 3 (ii))
• ☒ Direct and indirect mean (activity)

Total questions answered: 7 of 7