# Statistics of mathematics tangled with assortment, allotment,Statistics of mathematics tangled with assortment, allotment,

Statistics in Management Decision Making

BN171114

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West Cliff University

21/01/2018

Abstract

This paper explores about the statistics and its perspective in management decision making. Here I have explained about the basic concept of the statistics which is applied in the real world. This paper also includes concept of probability and its example. At last I have researched one manufacturing company which is using statistical tools which helped the company for better quality and quantity.

Statistics

Statistics is a section of mathematics tangled with assortment, allotment, analysis, and clarification of numerical certainty. Statistics is the application of data (Business Dictionary). There are compelling number true samples where statistics are worn. For example, you and a friend are at a basketball game, and out of the blue he proposes you a bet that neither team will bump a home run in that game. Should you take the bet? (Statistics/Introduction/What is Statistics)

There are mainly two types of statistics, descriptive statistics and inferential statistics. Descriptive statistics accord data that depict the information in some way. It administers a short synopsis judgment of information. Data can be encapsulated numerically or graphically as you want. For example, suppose a clothing shop sells pants, t-shirt and shocks. If 100 cloths are sold, and 40 out of the 100 were t-shirt, then one description of the data on the cloths sold would be that 40% were t-shirt. (Descriptive & Inferential Statistics: Definition, Differences & Examples)

In inferential statistics we benefit capricious illustration of data which are appropriated from a population to portray and provoke conjectures regarding the number. For example, if you want to know the average height of all the women in a town with a population of so many million residents. It will not be practical to get the height of each woman. In this case inferential statistics arrives into play. Inferential statistics are scarce when it is not appropriate or possible to review each member of a complete population. (Descriptive & Inferential Statistics: Definition, Differences & Examples)

A variable will be at whatever attribute, figure, or quantity that can be consistent or counted. A variable might furthermore be called a data component. Age, sex, business income and expenses, country of birth, capital expenditure, class grades, eye color and vehicle type are examples of variables. (What are Variables?)

Here is the flow chart of types of variables:

Numeric variables have amount that portray a perceptible quantity as a number, like ‘how many’ or ‘how much’. Therefore numeric variables are quantitative variables. Categorical variables have amount that portray a ‘quality’ or ‘distinctive’ of a data unit, like ‘what type’ or ‘which class’. Therefore, categorical variables are qualitative variables and contribute to be characterized by a non-numeric value. A continuous variable is a numeric variable. Conclusion can take any value between a convinced set of real numbers. The value given to a conclusion for a continuous variable can include values as small as the apparatus of analysis allows. Examples of continuous variables include height, time, age, and temperature. A discrete variable is a numeric variable. Conclusion can take a value based on a count from a set of definite whole values. A discrete variable cannot take the value of a fraction between one value and the next closest value. Examples of discrete variables include the number of registered cars, number of business locations, and number of children in a family, all of  which measured as whole units (i.e. 1, 2, 3 cars). An ordinal variable is a categorical variable. Conclusions can take a value that can be reasonably arranged or graded.  Examples of ordinal categorical variables include academic grades (i.e. A, B, C), clothing size (i.e. small, medium, large, extra-large) and attitudes (i.e. strongly agree, agree, disagree, strongly disagree). A nominal variable is a categorical variable. Conclusions can take a value that is not able to be coordinated in a cogent sequence. Examples of nominal categorical variables include sex, business type, eye color, religion and brand (What are Variables?)

Frequency table and its associated terms

Measurable information might comprise of a rundown for numbers identified with an exploration. Around the individuals’ numbers, few might a chance to be repeater twice furthermore actually more than double. Those tedious about amount may be information situated may be termed as frequency recurrence from claiming that specific amount alternately the variable to which that number will be doled out. Those frequencies of variables in information are will make recorded in a table. This table is known as frequency distribution table and the rundown has alluded as recurrence circulation. (Frequency Distribution)

Here are the types of frequency distributions:

Grouped frequency distribution: it is an arrangement class intervals and corresponding frequencies in a table.
Ungrouped frequency distribution: it is an interval width of 1 and arrangement of the observed values in ascending order. Data are not arranged in groups.
Cumulative frequency distribution: in this distribution, the frequencies are shown in the cumulative manner. It can be defined as the sum of all previous frequencies up to the current point.
Relative frequency distribution: If the frequency of the frequency distribution table is changed into relative frequency then frequency distribution table is called as relative frequency distribution table. For a data set consisting of n values.
Relative cumulative frequency distribution: It is the cumulative frequency divided by the total frequency (Frequency Distribution)

Example of a frequency table and relative frequency table

Performance

Frequency

Relative Frequency

Relative Frequency Percentage

Early

25

25/100=0.25

25%

On- time

64

64/100=0.64

64%

Late

9

9/100=0.09

9%

Lost

2

2/100=0.02

2%

Total

100

1

100%

Chart and Graph

Frequency distribution chart is a set of steep bars whose areas are commensurate to the frequencies. In the histogram, variable is consistently taken on the horizontal axis and frequencies on the vertical axis. The graphs are used to admit the attribute of discrete and continuous data. Two frequency distributions can be compared by the shapes and patterns. (Frequency Distribution)

There are two types of data and they are described as below:

Quantitative data: Quantitative data is numerical. For example, the number of pets, time of day, the temperature outside. It can be diagrammed. If you poll or part, you are assembling quantitative data. There are two types of quantitative data: discrete and continuous data.

Qualitative data: Qualitative is descriptive data. For example, the colour of a house, smell of a sock, texture of a shirt etc

Measure of Location

Mean, Median and Mode are the three mainly used measure of location.

1.      Mean: mean is synonymous with the average.  This is the best measure for symmetrical distributions. Mean is influenced by all data and most reliable. Mean is good for interval and ratio data.

2.      Median: the median is the value in the middle of a set of data. This is good for asymmetrical data. Median works for ordinal interval and ratio data. Median does not account for extreme scores. It is not algebraically defined.

3.      Mode:  the mode is the most frequent value, number or category in a set of data. One way to remember this definition is that mode sounds like most. The only appropriate measure that works for nominal data. Mode can be used for ordinal, interval and ratio data.

Measure of Dispersion

The measure of dispersion follows the measures of central tendency so the common measures of dispersion are standard deviation and variance.

Dispersion is the degree of variation in the data. For example, the age of instructors {48, 49, 50, 51, 52}

Range is the difference between the maximum and minimum observations. For example, the minimum age of an instructor was 29 and maximum age was 73.

Standard deviation is the square root of the variance. The variance is in square units so the standard deviation is in the same units as x

Displaying and Exploring data

A dot plot bands the data in as little arena as possible and classify of an individual conclusion is not lost. To evolve a dot plot, each observation is simply shown as a dot along a horizontal number line revealing the possible values of the data.

Stem and leaf: One technique that is used to array quantitative clues in a concise form is the stem and leaf array. It is a statistical technique to present a set of data. Each numerical value is cleft into two parts. The dominant digit becomes the stem and the hunting digit the leaf. The stems are located along the vertical axis and the leaf values are stacked against each other along the horizontal axis.

Box plot: it is a graphical array, planted on quartiles, that helps us picture a set of data. To construct a box plot, we need five statistics;

1.      The minimum value

2.      The first quartile (Q1)

3.      The median

4.      The third quartile (Q3) and

5.      The maximum value

Skewness: Another attribute of a set of data is the shape. There are four shapes commonly observed;

1.      Symmetric

2.       Positively skewed

3.       Negatively skewed

4.       Bimodal

The coefficient of skewness can range from -3 to +3. A value near -3, reveal negative skewness, a value such as 1.63 reveal moderate positive skewness and a value of 0, which will occur when the mean and median are equal, reveals the circulation is symmetrical and that there is no skewness present.

PEARSON’S COEFFICIENT OF SKEWNESS, sk=   3(x?- Median) / s

SOFTWARE COEFFICIENT OF SKEWNESS, sk = n / (n-1) (n-2) x ? (x-x?/s)3

Describing relationship between two variables:

When we review the connection between two variables we refer to the data as bivariate. One graphical approach we use to show the connection between variables is called scatter diagram. To stalemate a scatter diagram we need two variables. We scale one variable along the horizontal axis of a graph and the other variable along the vertical axis

Contingency Tables: A contingency table is a cross-tabulation that concurrently compile two variables of interest. For examples:

1.      Students at a university are classified by gender and class rank.

2.      A product is classified as acceptable or unacceptable and by the shift (day, afternoon, or night) on which it is manufactured. (McGraw/Hill, 2015)

Probability

Probability is analogous to percentage. Probability is a section of mathematics that deals with calculating the likelihood of a given event’s occurrence, which is assert as a number between 1 and 0 (TechTarget). When the probability is 0, that is an absurd event and if the probability is 1, that is a sure event. For example, when child will born, if the probability of girl child is 0.6 then the probability of boy child will be 0.4 because total should be 1.

Probability of an event = the number of ways event A can occur

The total number of possible outcomes

For example:

Here, we have to find the probability of either X and Y

P(X)=0.07

P(Y)=0.02

P(X or Y)=?

As we know,

The probability of either X and Y occurring is = P(X) +P(Y)

=0.07+0.02

=0.09

The probability of neither X and Y occurring is= 1-P

= 1-0.09

=0.01

The company that I have researched is manufacturing company of noodles. You can’t manage what you can’t measure. This company has been using statistics for the following functions:

·         To forecast the production, whether there is a stable demand and uncertain demand.

·         To know the risk that is associated within the operations and financial costs.

·         To calculate the given information to show the statistical outcome.

Statistics can help in increasing not only the quality of products but also the quantity that are being manufactured. Statistics can also help support the quality in the areas of the benefits of the business process, those mechanical and building processes. For the likelihood for similarity as considerably dependent upon date, and real time feedback, quality can be expanded almost instantly.