Consider the following for the two items that follow: The sum and the sum of squares of the observations corresponding to length X (in cm) and weight Y (in gm) of 50 tropical tubers are given as ΣX = 200, ΣY = 250, ΣX² = 900 and ΣY² = 1400.
Which one of the following is correct?
Cannot be determined from the given data
The variance of X and Y cannot be determined from the given data alone, as we only have the sums and sums of squares.
What is the median height of the class?
What is the total number of students whose height is less than or equal to 165 cm?
| LIST-I | LIST-II | |
| A. Sampling error | I. | Values that describe the characteristics of a population |
| B. Parameters | II. | The standard deviation of the sampling distribution |
| C. Sampling fraction | III. | Variation among sample statistics due to change |
| D. Standard error | IV. | Proportion of the population contained in a sample |
Given below are two statements one is labelled as Assertion (A) and the other is labelled as
Reason (R).
Assertion (A): Additive model considers the total of various components resulting in the given
values of the over all time series and it is stated as:
$Y=T+C+S+I$
Reason (R): Multiplicative model assumes that the various components interact in a
multiplicative manner to produce the given values of the over all time series and
can be stated as $Y=T \times C \times S \times I$
In the light of the above statements, choose the most appropriate answer from the options given
below:
Match List - I with List - II.
| List - I | List - II |
| A. Sample proportion P = x/n | I. $\frac{\sigma}{\sqrt{n}}$ |
| B. Sample variance $S_1^2 = \frac{1}{n-1} \sum_{i=1}^{n}(xi-x̄)^2$ | II. $\sigma^2 \sqrt{\frac{2}{n}}$ |
| C. Sample variance $S^2 = \frac{1}{n} \sum_{i=1}^{n}(xi-x̄)^2$ | III. $\sigma^2 \sqrt{\frac{2}{(n-1)}}$ |
| D. Sample mean $\bar{x} = \frac{1}{n} \sum_{i=1}^{n}xi$ | IV. $\sqrt{\frac{\pi(1-\pi)}{n}}$ |
Choose the correct answer from the options given below :