Accuracy: Much better control over data collection errors is possible with sampling than with a census, because a sample is a smaller-scale undertaking.
Timeliness: Another advantage of a sample over a census is that the sample produces information faster. This is important for timely decision making.
Amount of Information: More detailed information can be obtained from a sample survey than from a census, because it take less time, is less costly, and allows us to take more care in the data processing stage. Destructive Tests: When a test involves the destruction of an item under study, sampling must be used. Statistical sampling determination can be used to find the optimal sample size within an acceptable cost.
Random sampling provides equal chance to each individual member of the population to be selected for investigation. Random samples therefore are unbiased in their being representative of the population under investigation.
The central tendency is often measured by the mean because the other two measures namely median and node are almost the same for a homogeneous population having symmetric distribution. However, if the distribution is severely skewed, then one must use the median as a single value representing population, such as salary in your organization.
Q4. Why is standard deviation a better measurement of data variation than the range?
Standard deviation uses the entire data, while the range uses only the two extreme values. Therefore, range is sensitive not only to the outliers but less stable than standard deviation.
It is by definition that P(A|B) = P(A and B)/P(B) provided P(B) is non-zero.
Q6. Why is P(A or B or both) = P(A) + P(B) – P(AÇB)?
P(A or B or both) = P(only A) + P(only B) + P(both) =
[P(A) - P(both)] + [P(B) - P(both)] + P(both) =
Since the sum of the probabilities is not equal to one, it implies that these three events are not Simple Events. That is, at least one of the events is a composite event depending on at least one of the other events.
Q11. Why are stratified random samples “random”?
Q12. Why are cluster samples “random”?
Q14. Why the “margin of error” is often used as a measure of accuracy in estimation?
The half-length of the confidence interval is often referred to as absolute error, absolute precision, and even margin of error. However, the usual usage of the “marginal of error” is referred to the half-length of confidence interval with 95% confidence.
Most statistical models are not linear, however if we are interested in a small range then, almost all non-linear function can be approximated by a straight line.