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Statistics
What is statistics
Statistics

What is Statistics? I think every one of you came here to learn things about the topic of statistics. I can help you out. In today’s topic, I will tell you about What is statistics? Why do we study it? History of statistics How statistic is used in our everyday life. So, guys stay tuned.

From my perspective, statistics is a very interesting topic that can be used in day-to-day life, and today, I am here to give you complete information about the topic so that everybody can gain interest in statistics.

The practice or science of collecting and analyzing numerical data in large quantities, especially for the purpose of inferring proportions in a whole from those in a representative sample. Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting, and presenting empirical data.

I will try my best to make the topic easy and interesting for all of you. I will tell more about statistics and different types of skills used to solve the problems and the history of the topic in the upcoming paragraphs. So, let’s get started.

What is Statistics?

Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting, and presenting empirical data. Statistics is a highly interdisciplinary field; research in statistics finds applicability in virtually all scientific fields and research questions in the various scientific fields motivate the development of new statistical methods and theory. In developing methods and studying the theory that underlies the methods statisticians draw on a variety of mathematical and computational tools.

Two fundamental ideas in the field of statistics are uncertainty and variation. There are many situations that we encounter in science (or more generally in life) in which the outcome is uncertain. In some cases, the uncertainty is because the outcome in question is not determined yet (e.g., we may not know whether it will rain tomorrow) while in other cases the uncertainty is because although the outcome has been determined already we are not aware of it (e.g., we may not know whether we passed a particular exam).

History-:

Statistics, in the modern sense of the word, began evolving in the 18th century in response to the novel needs of industrializing sovereign states. The evolution of statistics was, in particular, intimately connected with the development of European states following the peace of Westphalia (1648), and with the development of, which put statistics on a firm theoretical basis.

In early times, the meaning was restricted to information about states, particularly demographics such as population. This was later extended to include all collections of information of all types, and later still it was extended to include the analysis and interpretation of such data. In modern terms, “statistics” means both sets of collected information, as in national accounts and temperature records, and analytical work which requires statistical inference. Statistical activities are often associated with models expressed using probabilities, hence the connection with probability theory.

The large requirements of data processing have made statistics a key application of computing. A number of statistical concepts have an important impact on a wide range of sciences. These include the design of experiments and approaches to statistical inference such as Bayesian inference, each of which can be considered to have its own sequence in the development of the ideas underlying modern statistics

Use of statistics in day-to-day life-:

Statistics play a big role in our daily lives, even without us knowing. Here are just a few examples.

  1. Census-:

A census is used to collect information about members of a population. The term mostly applies to national information, although a census can also refer to a survey of precise, small populations. For example, we could take a census of pig producers in the Northern part of Thailand, or musicians in European countries, or people aged 80 and above in Japan. An example that impacts trade is the annual economic census. Data are collected from individual businesses and are then compared and summarized. This information is then used to measure trends, and create estimates and forecasts, which allow businesses and policymakers to plan their business activities for several years ahead.

  1. Sampling-:

It is not always possible to collect data from every member of a population, so often a smaller sample is collected. For example, every few years data are collected by the World Health Organization (WHO) and the Food and Agriculture Organization of the United Nations (FAO) to learn about human health and agricultural products in different countries. These Government organizations use smaller, random samples to try to understand the characteristics of the whole population.

Words used in Statistics-:

Data -: A set of numerical facts collected with some definite object is called a set of data.

Variable-: A variable is a quantity that is measured in an experiment. Variate is a particular value of the variable.

Continuous Variable-: A variable that can take any value in a certain range.

Discontinuous variable-: A variable that cannot assume any value between two given values. It is also known as a discrete variable.

Raw data (ungrouped data) and Arrayed data-: Data collected in its original form are called raw data. The original data presented in a particular order(ascending or descending order) is called arrayed data.

Frequency-: The frequency gives the number of times a particular item occurs in a data.

Frequency distribution-:

The tabular arrangement of the given numerical data showing the frequency of different variates is called frequency distribution and the table itself is called frequency distribution table.

Note-:

  1. Exclusive series is that in which every class-interval excludes items corresponding to its upper limit.
  2. Inclusive series is that series which includes all items upto its upper limit.
  3. Class size is the difference of upper limit and lower limit in a class.
  4. Class mark is the mid-point of a class

i.e. , class mark = (Upper limit + Lower limit)/2

5. The sum of frequencies of a particular class and of all classes is called the cumulative frequency of that class or of all classes.

6. Tally marks/bars are the representation of frequency distribution of a class – interval. We put one vertical stroke corresponding to each item, when four strokes are drawn against a particular interval then the fifth stroke is drawn across these previous four making counting easier.

7. For the frequency distribution table, we make three columns.

A) Class-interval B) Tally marks C) Frequency

Conversion of discontinuous intervals to continuous intervals: To convert the discontinuous class into a continuous class we need adjustment. The value of the adjustment factor is calculated as below :

Adjustment factor

The lower limit of one class = Upper limit of the previous class/2

Subtract the adjustment factor from all the lower limits and add it to all upper limits.

Graphical Representation -:

Representing numerical data graphically becomes easier to understand than the actual data. These graphs show certain characteristics of the data at a glance. Among these are Bar graphs, Frequency Polygon, histograms, etc.

Bar Graph-:

Bar graphs are those diagrams in which data is represented in terms of bars or rectangles, Some of the features are :

  • All bars of a diagram are of the same breadth.
  • The height of the bars differ according to different values of the variable.
  • Bars are equidistant from each other.
  • All bars based on same common base line.

Histogram-:

The Histogram is a way of representing the data given in the class-interval form or you can say that, the graphical representation which organizes a group of data points into user-specified ranges. In this, adjacent rectangles are constructed taking width as the size of class-interval and length as the frequency of that class. Similar in appearance to a bar graph, the histogram condenses a data series into an easily interpreted visual by taking many data points and grouping them into logical ranges or bins.

Frequency Polygon :

When the mid-points of the adjacent tops of the rectangles of a histogram are joined by straight lines, the figure so obtained is called a frequency polygon. Both the sides of the frequency polygon are extended to meet the x-axis.

Frequency polygons can also be drawn independently without drawing histograms. For this, we require class marks i.e., mid-points of the class – intervals in the data.

Procedure to Draw Histogram-:

  1. Present the data in the form of exclusive class-intervals.
  2. Selecting a suitable scale, represent the class boundaries on the x-axis.
  3. Selecting a suitable scale, representing the frequencies on y-axis.
  4. Construct different rectangles having class boundaries as bases and corresponding frequencies as height.

Procedure to Draw Frequency Polygon-:

  1. Represent the class marks along the x-axis.
  2. Represent the frequencies along y-axis.
  3. Join these points in order by straight lines.
  4. Both the sides of the frequency polygon are extended to meet the x-axis.

Procedure to draw histogram and frequency polygon simultaneously on the same scale :

Follow the procedure as enumerated at points (2) and (3). Always draw Histogram first and frequency polygon afterward.

Mean-:

If there are n observations x1, x2, x3, . . . . xn in an ungrouped data.

then Mean ( x’) = (x1+x2+x3+ . . .+xn)/n = (i=1n xi)/n

Case 1. If x’ is arithmetic mean of n items x1, x2,. . . xn , then

i=1n (xi -x’) = 0

Case 2.

  1. Mean of ax1, ax2,. . . axn is ax’.
  2. Mean of x1/a, x2/a,. . ., xn/a is x’/a .
  3. Mean of xi +– a, x2 +– a, . . . . xn +– a is x’ +– a.

Median-:

Median divides the given data into two equal parts, one part contains values that is more than the median and the other part with values less than the median.

For determining the median, we first arrange the data in ascending or descending order.

  1. If N is odd, then Median

= Value of ((N+1)/2)th item.

2. If N is even, then Median

= 1/2 [(N/2)th item + (N/2+1)th item], where N denotes number of items.

You can also check out my other articles https://stormypassion.com/what-is-co-ordinate-geometry/.

For trigonometry open the link https://stormypassion.com/trigonometry-best-used-formulas/.

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