Page 169 - Data Science class 10
P. 169
Figure below is an illustration of the relationship between samples and populations:
Research is meant for But actually made
this size on this amount
Random selection
Sample
Popluation Inference
Parameter μ X Statistic
(Population mean) (Sample mean)
For example, let's imagine you're interested in learning the median income of magazine subscribers in
general—this is a population parameter. You draw a random sample of 100 subscribers and determine that their
mean income is $27,500 (a statistic). You conclude that the population mean income μ is likely to be close to
$27,500 as well. This example is one of statistical inference.
Different symbols are used to denote statistics and parameters, as shown in the following table:
Sample Statistic Population Parameter
Mean x m
Standard deviation s sigma
Variance s 2 sigma 2
The information obtained from the statistical sample allows statisticians to create hypotheses about the wider
population. In statistical equations, population is usually denoted with an uppercase N while the sample is usually
denoted with a lowercase n.
3.4.2. Standard Deviation
The standard deviation is the variation in the population that is inferred from the variation in the sample. When the
standard deviation is divided by the square root of the number of observations in the sample, the result is referred
to as the standard error of the mean.
In statistics, probability is a very important tool. The nature of the two situations will show the differences between
them.
Problem 1: Assume a coin is “fair”. Question: If a coin is tossed 10 times, how many times will we get “tail” on the
top face?
Problem 2: You pick up a coin. Question: Is this a fair coin? Or, does each face have an equal chance of appearing?
Problem 1 is a mathematical probability problem. Problem 2 is a statistics problem that can use the mathematical
probability model determined in Problem 1 as a tool to seek a solution. The answer to neither question is
deterministic.
Identifying Patterns 167

