Question

The degree to which numerical data tend to spread about a value is called
\[{\text{(A) mean}}\]
\[{\text{(B) variation}}\]
\[{\text{(C) median}}\]
\[{\text{(D) mode}}\]

Answer 1

Hint: In this question we will elaborate the meanings of all the various given tendencies and then conclude the required answer.

Complete step by step solution:
Mean of a distribution is the sum of all the terms in the distribution divided by the number of terms in the distribution, it gives no information of how the data tend to spread.
Median of a distribution represents the middle value of the numerical distribution when the distribution is arranged in an ascending order.
Mode of a distribution gives us the most frequent term in the distribution i.e. the term or value which is presents the maximum number of times.
Variance tells us how much the data spreads from a value, it shows us how similar or non-similar the data are in the distribution. The variance could be from any value in the distribution but is usually calculated from the values such as mean, median and mode.

Therefore, the correct option is $(B)$

Note: Variance is independent of change of origin as the change in origin is uniformly added to all the values and hence the mean also and hence, when ${(x - \bar x)^2}$ is calculated there is no change in the overall answer.
Arithmetic mean should not be used when there are some extreme values in the distribution, since there are no extreme values over here, the formula of mean can be used to calculate the missing value.
Mean is just the word used for average, it is the word used mostly by people in daily life and it just represents the central value of distribution.