An index number is primarily used in statistics to accomplish which of the following objectives?

In a moderately skewed distribution, if Mean = 12 and Median = 8, then using Empirical relation (Mode = 3 Median - 2 Mean), what is the value of Mode?

If 4y - 5x = 15 is the regression line of y on x and the coefficient of correlation between x and y is 0.75, what is the value of the regression coefficient of x on y (bxy)?

Which measure of dispersion is based on taking absolute deviations of observations from a measure of central tendency?

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): In hypothesis testing, a Type I error occurs when a true null hypothesis is rejected. Reason (R): The level of significance represents the probability of committing a Type I error. In the light of the above statements, choose the most appropriate answer from the options given below:

The mean deviation of a dataset about its mean is zero if:

The standard deviation of a sample of 20 observations is 5. If a constant value 2 is added to each observation, then the standard deviation of the resultant sample is:

The range for the dataset 4, 9, 14, 20 is:

The weights (in kg) of 50 students are distributed in continuous classes: x-40, 40-50, 50-60, 60-70, 70-80, with frequencies 5, 10, 15, 12, 8 respectively. If the range of the data is 45 kg, then the value of x is: