Question

Consider the following statements. Which of these is/are correct?
A) Mode can be computed from histogram.
B) Median is not independent of change of scale
C) Variance is independent of change of origin and scale
D) None of these.

Answer 1

Hint- In order to solve such problems students must use the basic concept and definition of statistics. The problem can be solved by visualizing the statement with some examples.

Complete step-by-step answer:
A histogram is an approximate representation of the distribution of numerical. It was first introduced by Karl Pearson. To construct a histogram, the first step is to "bin" the range of values—that is, divide the entire range of values into a series of intervals—and then count how many values fall into each interval.
Change of origin means some value has been added or subtracted in the observation. Change of scale means some value is multiplied or divided by observations.
The mode of a set of data values is the value that appears most often. As in the histogram there is the representation of all the data values along with its frequency. So, mode can be easily computed from histogram. We can see the highest frequency so made.
So, option A is correct.
Median is the middle number in a sorted list of numbers. If there is an odd amount of numbers, the median value is the number that is in the middle, with the same amount of numbers below and above.
So, if we change the scale definitely the middle number will change and hence the median will also change.
So, option B is also correct.
Variance is the expectation of the squared deviation of a random variable from its mean. Informally, it measures how far a set of numbers are spread out from their average value.
So, variance remains the same even if we change the origin and scale.
So, option C is incorrect.
Hence, mode can be computed from histogram and median is not independent of change of scale.
So option A and option B are correct options.

Note- An extension of the bar graph is the histogram. A histogram is a type of vertical bar graph in which the bars represent grouped continuous data. The shape of a histogram can tell you a lot about the distribution of the data, as well as provide you with information about the mean, median, and mode of the data set. Students must remember the basic definition related to statistics in order to visualize the mean, median, mode directly from histogram.