Compare the following two ratio scale data sets using suitable graphical analysis tool: Score before training: 12, 17, 15, 23, 27, 21, 24, 19, 20, 23, 16 Score after training: 16, 22, 20, 24, 30, 20, 30, 17, 27, 31, 19 Also interpret the finding on the basis of the graph.

If A = {3, 6, 9, 12, ...} and B = {15, 30, 45, ...} then verify whether two sets A and B are equivalent or not.

Comment on the height of a bar in a bar diagram and height of a bin in a histogram. Are two heights have the same meaning? Explain it with the help of an example

An institution made a policy for delay of payment beyond a certain date to be paid by its customers. Penalty as per policy are as follows: Rs 50 for the first day, Rs 100 for the second day, Rs 150 for the third day, and so on. If a customer makes the payment on a delay of 31 days then how much he/she has to pay as penalty charges.

Distinguish characteristic features of each of the four measurement scales: (I) Nominal (II) Ordinal (III) Interval, and (IV) Ratio Scale. Name the measurement scale for each of the following variable.

i) Waiting time for a bus at a particular bus stop in a certain city.

ii) Number of pages in a book.

iii) Temperature in degree Celsius.

iv) Classification of cancer patients according to their severity of diseases. v) Monthly income of the family

vi) Saving (Income in that particular month − expenditure in the same month) of the family. Keep in mind that expenditure may be more than income in that particular month of some family(ies)

vii) Temperature of water by touch: cold, lukewarm and hot

viii) Height of students of a class

ix) State of residence of each student of PGDAST programme

x) Balance of Smart card of Delhi Metro hold of different passengers

Discuss the continuity and differentiability of the following function at x = 5.

If in a hall there are 10 randomly selected students then how many numbers of ways are there such that all of them have different birthday. Assume that all of them have their birth day in non-leap years