Which of the following statements are true? Give reasons for your answer.

(i) F-distribution is always used in goodness of fit.

(ii) Measure of central tendency in a data set refers to the extent to which the observations are scattered.

(iii) A process is said to be under assignable cause when the points are above the VCL link of ( chart. X,R)

(iv) Simple random sampling is done by using random number tables where the probability of drawing a digit is .1 0⋅ (v) All time series have a trend.

Let's examine each of the statements one by one and determine whether they are true or false, providing reasons for our answers.

(i) F-distribution is always used in goodness of fit.
False.
The F-distribution is not always used in goodness of fit. Goodness of fit tests typically involves comparing observed data to a theoretical distribution, such as the normal distribution or the chi-squared distribution. The F-distribution is commonly used in analysis of variance (ANOVA) tests, which assess the differences between group means. It is not directly associated with the goodness of fit tests.

(ii) Measure of central tendency in a data set refers to the extent to which the observations are scattered.
False.
A measure of central tendency, such as the mean, median, or mode, provides information about the center or typical value of a dataset, but it does not describe the extent to which the observations are scattered. Measures of spread, such as standard deviation or ________ ___ __________ _______ ______ _______ ___.
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