Statistics is a field of study that deals with data collection, analysis, interpretation, and presentation. Statistics can help you make informed decisions, from market research and business operations to scientific experiments and social trends.
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Statistics is an indispensable tool for almost any field – from biology to business, nursing to marketing. Statistics is used in almost every profession. Marketers can use it by following the four step Statistics process to understand consumer habits, social scientists to study human behavior, and even artists who want to understand the general reception of their work. Statistics majors are also some of the most marketable courses because many fields use statistics as a key component in their research and analysis today. In this article, we will explore more about what is statistics.
These are the numerical measures that measure quantitative data. The measures may include:
- Mean – is the expected value of a set of numbers. It can be expressed as the sum of values divided by the number of values.
- Median – is the value of a set of numbers where half of the numbers are smaller, and half are larger.
- Measures of Variation – is the amount that values deviate from the mean (i.e., variance and standard deviation)
- Mode – is the most frequently occurring value in a set of numbers. Here you look for the most recurring value in the given values.
- Standard deviation – is the square root of variance. It measures the dispersion of data around their mean and how much values vary from the mean.
- Variance – is the average squared difference between observed values and the mean. Variance is the most important measure of dispersion.
- Percentiles – are the values of a set of numbers to which 50% of the observations fall below and the other 50% fall above at least once. Percentiles are also known as deciles.
However, there are many more statistical measures used in Data Analysis; the above mentioned are some examples.
Branches of Statistics
There are two main categories of statistics. They include:
- Descriptive Statistics
- Inferential Statistics
Descriptive statistics are used to describe the data you got. Statistics deals with discovering patterns and trends in a data set. It includes descriptive statistics like mean, median, mode, and standard deviation. Mathematically, these statistics are called parameters because they are values that describe the data set. Descriptive statistics help to understand the data better. Most people use descriptive statistics to repurpose the tricky quantitative insights into understandable bite-sized descriptions.
Descriptive statistics is further divided into three categories. These three include frequency distribution, measures of variability, and measures of central tendency.
1. Frequency Distribution
The frequency distribution of data is the number of values in that data. It involves the use of a histogram. The histogram gives an idea of how common the data point is. For example, if we have x=50, the frequency distribution will be [50, 10, 30, 30, 10] for a data set. The frequency distribution shows the number of different values that the data set can be divided into. The classic histogram is a simple way to present a frequency distribution. Other charts and graphs used to represent frequency distribution include bar charts, line charts, and pie charts.
2. Measures of variability
Measures of variability show the spread of values in a data set. These are used to understand the variation in the data so that we can compare different points. Measures of variability include range, standard deviation, interquartile range, and variance. Range is the difference between a data set’s lower and upper limits. For example, if you have 2 values, 1=10 and another 2=20, the range will be 10-20 (if the difference between both items is calculated for 0).
Range tells us where most of the data lies. Standard deviation indicates how often each value occurs in our data set. Standard deviation appeared first and was also one of the first measures developed to explain fluctuations in financial markets (such as prices and returns). The interquartile range shows how much less than half a sum is left (3rd quartile) or greater than half a sum (1st quartile).
Variance shows how much our data set varies between two extreme values plotted against each other. Variance shows more variation across values, indicating spread or dispersion in terms of its extreme values compared to standard deviation.
3. Measures of central tendency
Measures of central tendency are based on 3 values: mean, median, and mode. Mean is the arithmetic average. It summarizes a data set in the sense that it can be associated with all the values. It’s also called “arithmetic mean” because it is calculated as an average (sum divided by the number of values). For example, if you have a set of values 2, 3, 4, 5, 6, 7, the mean will be calculated as (2+3+4+5+6+7) divided by 6.
Median is a middle point between two or more sets of numbers. Median is middle when we sort our data points according to whatever rule we want before calculating or picking the middle value. That means the median is not necessarily the same as the mean. Like the example above, the median would be (4+5) divided by 2 when the values are arranged in ascending order. You have to first arrange the values in the required order and find the middle value that stands alone. That is the median. If the middle values are two and not one, you must find their average, as in our example above.
Mode is the value that appears most often in our data set. It’s also called the relative frequency (ratio) of occurrences of a value. If we have a dataset where the values are 1,4,4,4,4,5, and the mode is 4, then the mode appears 4 times in our dataset. Density is a special case of mode. It’s calculated so that for every value, you can find how frequently it appears in your data set. You could find the probability for each value to appear in your dataset. However, you usually don’t need this kind of information. The density gives you a single number proportional to how many times a value appears in your dataset.
Inferential statistics is an important branch of statistics, sometimes called mathematical statistics. Using inferential statistics, you can test your hypotheses about a particular dataset. This category of statistics uses analytical tools to find conclusions about a data set or population by looking at random samples.
One of the most important inferential statistical tools is the confidence interval. A confidence interval tells you how likely your data set is to fall within a particular value or range of values.
Inferential statistics can be subdivided into two broad categories. These include regression analysis and hypothesis testing.
1. Regression Analysis
Regression analysis is used to find the relationship between two variables. A simple example would be comparing your weight changes based on height. One of the variables is your height, and another is how much you weigh.
Regression analysis can be used to find trends in data, estimate a variable’s value, or find the best fit line for a particular data set. You can also use this technique to determine the effect of an intervention (minor change) on a particular outcome (major change). Regression analysis can be categorized into linear, logistic, nominal, and ordinal. However, the most common is linear regression. Linear regression is used to infer the relationship between variables, usually through a linear mathematical function.
Linear regression refers to the weighted addition of a specific variable (or multiple variables) to a constant (independent variable) to measure its effect on an outcome variable. When binary data are being analyzed, two types of regression analysis are available: log-linear regression and quadratic, or partial, least squares (PLS). Both approaches can be used for predictive modeling purposes and classification problems. Among the important formulas to remember in regression analysis is the straight-line equation given by y=mean + standard deviation of the data set. These values are typically the regression coefficients.
2. Hypotheses Testing
Hypotheses testing is a statistical procedure that tests whether some variables influence the dependent variable and can be used to determine if there is a relationship between two variables. It is a method that tests whether there is a linear, quadratic, or other nonlinear relationship between two variables.
The standard of hypothesis testing depends on the assumed relationship between the dependent and independent variables. Hypotheses testing involves null and alternative hypotheses. The null hypothesis is that the correlation coefficient (r) returns a value of zero or one. The alternative hypothesis states that r returns a nonzero value. If the null hypothesis holds, we do not reject it; if it does not, we reject it. The rejection sample size will depend on predetermined criteria and should reflect outcomes for different sample sizes for various alternatives.
Some crucial hypotheses tests in inferential statistics include:
- Z test – The Z test is used to test whether the mean of one population does not equal the mean of another.
- Chi-Square test – The Chi-Square test compares an event’s occurrence in two or more populations.
- Null Hypothesis Test – In this hypothesis, we assume that all the observations are from a single population and that all observations are independent.
- One Sample T Test – This hypothesis is important when we have a sample that has only one value, and we want to find out if it follows a random process and if there is no difference between the two values that are observed in each sample by calculating the statistic coefficient (F) between two samples.
- Confidence interval – Here, the data is assumed to be continuous and normally distributed. The confidence interval is a range of values we can expect if the population parameter is assumed to be a true and normal distribution.
Statistics is a broad subject that of importance in our everyday life as it helps you find accurate information about any particular problem. It can be used in different situations such as in research work, business, science, government, and many more disciplines. Science uses statistics to understand the life on our planet and the universe at large. With the help of this article, you will learn about the different types of statistics, including their significance, applicability, and application.