 # Statistics

A numerical or graphical representation of data

## What is Statistics?

Statistics is a term that is derived from the Latin word “status,” which means a group of figures that are used to represent information about a human interest. It refers to the technique that is developed for the purpose of collecting, reviewing, analyzing, and drawing conclusions from quantified data. The data obtained is then used in the decision-making process.

Financial Analysts use statistical methods to analyze, evaluate, and summarize large volumes of data into a mathematical form that is useful. Statistics is applied in numerous disciplines such as business, social sciences, manufacturing, psychology, etc. ### Types of Statistics

The study of statistics is grouped into two main categories. They include descriptive and inferential statistics.

#### 1. Descriptive statistics

Descriptive statistics describe the basic features of a population and how the data is organized. This enables analysts to see the characteristics of data and make sense of that data. For example, assume a computer shop sells electronic devices, and out of the 1,000 electronic devices sold, 300 are laptops. With this data, one description of the data would be 30% of the sample represents laptops.

There are two main types of descriptive statistics that scientists use, and they include:

Measures of central tendency

Central tendency measures comprise the mean, median, and mode. They are used to show the general trends with the data. The mean is used to show the average of all the components of a data set, while the median represents the middle of the data such as the middle age of students going to college. The mode is used to show the most common data in a population, such as the most common age of students in their first year of college.

Measures of spread show how similar or different a set of values are and how they relate to each other. Some of the statistics used to describe how data is spread out include range, quartiles, variances, absolute deviation, frequency distribution, and standard deviation.

For example, in a class of 20 students, the mean score for a mathematics paper may be 70 out of 100 marks. Although the average is 70 marks, it does not mean that all students will score 70. Rather, it means that the scores will be spread out, both below and above the average score. In this case, the measures of spread are used to show how the scores are distributed.

#### 2. Inferential statistics

Inferential statistics use complex mathematical computations to infer trends about a large population. When analyzing a large population, it is difficult to analyze each member of that population one by one. Rather, scientists use inferential statistics to determine the relationships between variables in a sample population and then use the information to make predictions about how the variables relate to the general population.

For example, if scientists are analyzing the number of married men in a population of one million men, they will collect a sample from the population of one million men, and then make generalizations about the whole population based on the information obtained from the sample.

The two main classifications of inferential statistics comprise the following:

Confidence interval

The confidence interval is calculated from the statistics of observed data that may contain the actual value of an unknown population parameter.

Hypothesis testing

Hypothesis testing occurs when scientists analyze a sample of a population and then use that information to make a claim about the large population where the sample belongs to.

To learn more about the different foundational concepts for running a statistical test and interpreting the results, go to CFI’s Statistics Fundamentals course!

### Properties of Statistics

Some of the potential characteristics that a statistic should include:

#### 1. Completeness

Completeness refers to an indication of whether or not the data required to meet the information demand is available in the data resource. Completeness of data is necessary to ensure the accuracy of the observed data.

#### 2. Consistency

Consistency is viewed in terms of the uniformity or stability of data. Some of the statistics used to measure consistency include standard deviation, range, and variance. When measuring the consistency of data from a sample that is representative of a large population, the standard error of the mean is usually examined.

Also, when using instruments to collect data, consistency can be measured by estimating the reliability of the obtained scores.

#### 3. Sufficiency

A statistic is considered sufficient if there is no other statistic that can be computed from the sample. The sufficiency concept is common in descriptive statistics due to its strong dependence on the assumption of the data distribution form.

#### 4. Unbiasedness

The bias of statistics is determined by the difference between the true value of the parameter being measured and the estimator’s expected value. If the mean of the sampling distribution and the expected value of the parameter are equal, the statistic is considered to be unbiased.