Question

In: Statistics and Probability

Using your textbook, LIRN, JSTOR, other electronic journals and/or periodicals, and the Internet, develop an APA...

Using your textbook, LIRN, JSTOR, other electronic journals and/or periodicals, and the Internet, develop an APA paper that provides an in-depth analysis - complete with examples and research-based in-text citations to include the following topics:

How statistics is used by business to assist in making more effective decisions

Characteristics related to all type of statistics (descriptive and inferential) such as populations, samples, types of variables, levels of measurement, etc.

Frequency tables and distributions, including histograms and frequency polygons

Central tendency, to include the arithmetic mean and median values, mode, geometric mean, and standard deviation

The displaying of data and statistical results, such as box plot, stem-leaf, etc.

The concept of probability and the various types of events

Solutions

Expert Solution

Population:

The group of individuals under study is called ‘Population or universe’.

The number of individuals belonging to a population is called population size and it is denoted by N.

Eg. Trees in the jungle, Stars in the sky.

Sample:

A finite sub group of a population is called a sample.

The number of individuals in a sample is called sample size or sample number, it is denoted by n.

Eg. Testing of crackers and explosives, testing the life of an electric bulb or tube.

Types of Variables:

A measurable characteristic which changes its value is called a variable.

eg. age, height, weight, population, income etc.

There are 2 types of varibles.

  • Discrete Variable:A variable which can assume only some specific values within a given range is called a discrete variable. eg. No. of student in a class, No. of members in a family etc.
  • Continuous Variable: A variable which takes each and every value within a given range is called a continous variables. eg. Height, weight, age, income etc.

Levels of Measurement:

  • Nominal: Attributes are only named weakest.
  • Ordinal:Attributes can be ordered
  • Interval: Distrance is meaningfull
  • Ratio: Absolute Zero

Frequency:

The no. of times a perticular value of a variable is repeated in the data is called frequency of that value. it is denoted by f.

Class frequency: The no. of items which belong to a perticular class of a variable is repeated in the data is called class frequency of that value. it is denoted by f.

sum of frequency of all classes of the same data is equal to total no. of observations. i.e.

Frequency Distributions:

The value of variable arranged in order of magnitude (either individual or in groups) with respective frequencies side by side is called a frequency distributions of that variable.

it helps the computation of various statistical measures.

Central Tendency: A single numerical no. which is represent the whole data is called central tendency.

Mean: sum of all observation divided by total number of observation

Uses: The operation cost, profit per unit of an article, output per man and per machine, average per monthly income and expenditure etc.

Median: The value of the observation which lies at the centre, when data are arranged in ascending or descending order of magnitude.

Uses: in those cases where numerical measurement are not possible. Eg. Skill, honesty, intelligence etc.

Mode: The value of the observation which occur most repeated.

Uses: Ideal size for shoes and shirts, most popular fashion, business forecasting etc.

Geometric Mean: the 'n'th root product of 'n' numbers.

Uses: present value and future value cash flow formulas, to determine the performance results of an investment

Standard Deviation: It is the square root of the Variance. Variance is the expectation of the squared deviation of a random variable from its mean.

Histogram: It is represents a frequency distribution by means of rectangles whose widths represent class intervals and whose areas are proportional to the corresponding frequencies.

Frequency Polygaon: start just as for histograms, by choosing a class interval. Then draw an X-axis representing the values of the scores in your data. Mark the middle of each class interval with a tick mark, and label it with the middle value represented by the class. Draw the Y-axis to indicate the frequency of each class. Place a point in the middle of each class interval at the height corresponding to its frequency.

Uses: the shapes of distributions. They serve the same purpose as histograms, but are especially helpful for comparing sets of data

Box Plot: Uses: a simple way of representing statistical data on a plot in which a rectangle is drawn to represent the second and third quartiles, usually with a vertical line inside to indicate the median value. The lower and upper quartiles are shown as horizontal lines either side of the rectangle.

Probability: If a trial results in any one of n mutually exclusive, equally likely and exhaustive cases and if m of them are favourable to the event A, then probability of A denotedvby P(A) is given by,


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