Data Processing — NCERT Solutions

The advantages of mode are: it shows the most frequently occurring value in a data set, so it is easy to understand; it is not affected by extreme values; and it is useful when the data are qualitative or when we want the most common item, such as the most common crop, colour, or size. It is also suitable for identifying the typical value in a distribution with repeated observations.

In a normal distribution, the curve is symmetrical. Therefore, mean = median = mode. All three measures coincide at the centre or hump of the distribution. The scores are balanced equally on both sides.

In a positively skewed distribution, the tail stretches to the right. The usual order is mode < median < mean. The mean is pulled toward the higher values.

In a negatively skewed distribution, the tail stretches to the left. The usual order is mean < median < mode. The mean is pulled toward the lower values.

So:

• Normal distribution: mean = median = mode
• Positive skew: mode, median, mean from left to right
• Negative skew: mean, median, mode from left to right

A student may draw a symmetrical bell curve for the normal distribution and two asymmetrical curves for positive and negative skew, marking the positions of mean, median, and mode accordingly.

The applicability of mean, median and mode depends on the nature of data.

• Mean is the most useful when all observations are important and the data are fairly balanced. It is widely used because it is easy to compute and uses every value. But it is affected by extreme values, so it is not suitable for highly skewed data.
• Median is useful when the data contain extreme values or are skewed, because it is not disturbed much by very large or very small values. It is also suitable for positional data. However, it does not use all observations.
• Mode is useful when we want the most common value. It is especially helpful for qualitative data and for identifying the most frequent category. But a data set may have no mode, one mode, or more than one mode, so it is not always a stable measure.

Thus, no single measure is best for all cases. The choice depends on the type of data and the purpose of study.