# NCERT Solutions for Class 9 Maths Chapter 14 – Statistics PDF

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## Statistics and it's history in our society

### Population vs. sample

In statistics, a population is the set of all objects (people, etc.) that one wishes to make conclusions about. In order to do this, one usually selects a sample of objects: a subset of the population. By carefully examining the sample, one may make inferences about the larger population.

For example, if one wishes to determine the average height of adult women aged 20–29 in the U.S., it would be impractical to try to find all such women and ask or measure their heights. However, by taking small but representative sample of such women, one may determine the average height of all young women quite closely. The matter of taking representative samples is the focus of sampling.

## Randomness, probability and uncertainty

The concept of randomness is difficult to define precisely. In general, any outcome of an action, or series of actions, which cannot be predicted beforehand may be described as being random. When statisticians use the word, they generally mean that while the exact outcome cannot be known beforehand, the set of all possible outcomes is known — or, at least in theory, knowable. A simple example is the outcome of a coin toss: whether the coin will land heads up or tails up is (ideally) unknowable before the toss, but what is known is that the outcome will be one of these two possibilities and not, say, on edge (assuming that the coin cannot stand upright on its edge). The set of all possible outcomes is usually called the sample space.

The probability of an event is also difficult to define precisely but is basically equivalent to the everyday idea of the likelihood or chance of the event happening. An event that can never happen has probability zero; an event that must happen has probability one. (Note that the reverse statements are not necessarily true; see the article on probability for details.) All other events have a probability strictly between zero and one. The greater the probability the more likely the event, and thus the less our uncertainty about whether it will happen; the smaller the probability the greater our uncertainty.

There are several basic interpretations of probability used to assign or compute probabilities in statistics:

Relative frequency interpretation: The probability of an event is the long-run relative frequency of occurrence of the event. That is, after a long series of trials, the probability of event A is taken to be:

To make this definition rigorous, the right-hand side of the equation should be preceded by the limit as the number of trials grows to infinity.
Subjective interpretation: The probability of an event reflects our subjective assessment of the likelihood of the event happening. This idea can be made rigorous by considering, for example, how much one should be willing to pay for the chance to win a given amount of money if the event happens. For more information, see Bayesian probability.

### Classical approach to assigning probability

This approach requires that each outcome is equally likely. In this case, the probability that event A occurs is equal to the number of ways that A can occur divided by the number of possible outcomes of the experiment.
Note that the relative frequency interpretation does not require that a long series of trials actually be conducted. Typically probability calculations are ultimately based upon perceived equally-likely outcomes — as obtained, for example, when one tosses a so-called "fair" coin or rolls or "fair" die. Many frequentist statistical procedures are based on simple random samples, in which every possible sample of a given size is as likely as any other.

### Prior information and loss

Once a procedure has been chosen for assigning probabilities to events, the probabilistic nature of the phenomenon under consideration can be summarized in one or more probability distributions. The data collected is then viewed as having been generated, in a sense, according to the chosen probability distribution.