Attempt all the problems shown below. Word limit for each of the problem is around 500 words.

problem 1: Describe the meaning of statistics and describe its scope and use.

problem 2: Describe hypothesis testing and illustrate the general procedures for hypothesis testing.

problem 3: Tabulate the given 25 scores into a frequency distribution by using a suitable interval.

64, 69, 84, 67, 61, 72, 72, 63, 71, 83, 70, 76, 75, 81, 66, 73, 86, 65, 68, 81, 72, 67, 77, 75, 72

problem 4: Describe the concept of dispersion and describe the kinds of measures of dispersion.

problem 5: find out the average deviation and standard deviation from the given ungrouped data.

45, 43, 46, 47, 36, 39, 35, 45, 34, 47, 30, 35, 36, 39, 42, 44, 46, 38, 34, 35

problem 6: find out mean, median and mode for the given frequency distribution.

problem 7: Find out the correlation coefficients for the given data by using product moment method and deduce the coefficients.

problem 8: describe in detail the chi square test and elucidate its properties and application.

problem 9: Describe the term normal distribution in detail with focus on its characteristics and properties. Further elucidate the deviations from normal distribution curve with the help of diagrams.

problem 10: A group of 20 students were given mathematical test under two conditions: restricted and unrestricted position. Test the importance of the difference between mean at 0.01 level on the basis of the given data.