Overview of Descriptive Measures



Overview of Descriptive Measures


Measures of Central Tendency



·         A mean is the most common measure of central tendency.

  • A mean is what we commonly think of as the ‘average’ value.
  • Calculate the mean by summing the values and dividing by the total number of values.

90+80+70+85+70 = 395

Mean = 395/5 =  79

·         Extremely large values in a data set will increase the value of the mean, and extremely low values will decrease it.

  • To calculate a weighted mean, first, multiply each cell frequency by its weight or by the cell frequency, and then sum and divide by the total frequency.



X f f * X
90 1 1*90 = 90
80 2 2*80 = 160
70 3 3*70 = 210
85 2 2*85 = 170
70 1 1*70 = 70

Mean = 700/5 =    140




·         The median is the central point of the data.

·         Half of the data has a lower numerical value than the median.

·         Half of the data has a higher numerical value than the median.

·         The median is not affected by extremely large or small values.

·         To find the median, arrange the data in order from smallest value to largest value,  and

Þ       if there are an odd number of points, find the value that is in the center of the data

Þ      if there are an even number of points, add the two middle values and divide by 2.


For the values (written in order):          70  70  80  85  90

the median is 80.

  • The mode is the data value that occurs most frequently.
  • The mode is not affected by extreme values.


For the values:         70  70  80  85  90

the mode is 70.



Measures of Spread



·         Subtract the smallest value from the largest – or

·         Report the smallest and largest values.

Variance/Standard Deviation

·         The standard deviation is the average variation of the data values from the mean of the values.

·         The standard deviation is found by taking the square root of the variance, and the standard deviation is more useful than the variance in reporting results so it is the measure that is typically reported.


X X – Mean   (X – Mean)2
90 90-79 = 11 11*11 = 121
80 80-79 = 1 1*1 = 1
70 70-79 = -9  -9*-9 = 81
85 85-79 = 6 6*6 = 36
70 70-79 = -9  -9*-9 = 81
395 320
Mean = 395/5 = 79
Sample Variance = 320/4 = 80
Sample Standard Deviation = 8.9
Population Variance = 320/5 = 64
Population Standard Deviation = 8.0



The Empirical Rule

·         Apply this rule to interpret the measures when the data is symmetrical.

·         At least:

68% of the data values are within one standard deviation of the mean

90% of the data values are within two standard deviations of the mean

99% of the data values are within three standards deviation of the mean

Tchybychef’s Inequality

·         Apply this method to interpret the measures when the data is skewed.

·         At least:

75% of the data values are within two standard deviations of the mean.

90% of the data values are within three standard deviations of the mean.




Measures of Relative Standing



If your percentile score on the GRE is 90 then you scored better than 90% of those taking the test, and you scored lower than 10% of those taking the test,


·         The lower quartile is the same as the 25th percentile.

Þ      25% of the scores are lower and

Þ      75% of the scores are higher than the lower quartile.

·         The upper quartile is the same as the 75th percentile.

Þ      75% of the scores are lower and

  • 25% of the values are greater than the upper quartile.



  • Correlation is used in describing the strength of the relationship between two (or more) variables.
  • There are many different types of correlation coefficients and selection of the appropriate one depends on the form of the variables. We will consider Pearson Product-moment Correlation Coefficient which assumes continuous quantitative data.
  • Correlation coefficients reflect whether the relationship between variables is:
  • positive (i.e. as one variable increases, the other variable increases) or
  • negative (i.e. as one variable increases, the other variable decreases).

It also may indicate that there is no relationship.


  • Borg and Gall, Educational Research from Longman Publishing, provide the following information for interpreting correlation coefficients.
  • Correlation coefficients ranging from 0.20 to 0.35 show a slight relationship between the variables; they are of little value in practical prediction situations.
  • With correlation around 0.50, crude group prediction may be achieved. In describing the relationship between two variables, correlation coefficients that are this low do not suggest a good relationship.
  • Correlation coefficients ranging from 0.65 to 0.85 make possible group predictions that are accurate enough for most purposes. Near the top of this correlation range, individual predictions can be made that are more accurate than would occur if no such selection procedure were used.
  • Correlation coefficients over 0.85 indicate a close relationship between the two variables.


  • It is important to understand that even a high correlation coefficient does not establish a cause and effect relationship. There may be other factors that relate to both of the variables.
  • In comparing two variables, you can take the square root of the correlation coefficient to get the Coefficient of Determination; this measure gives the percent of the variation in the dependent variable that is ‘explained’ by the independent variable.
  • It is always good to look at an XY scatter plot to see what you think about the relationship between the variables.
  • Excel will not only give you a correlation coefficient, but it will also give you the equation for the Least Square line which can be useful in describing the relationship between the two variables and in making predictions of the dependent variable from the independent variable.


Get Professional Assignment Help Cheaply

Buy Custom Essay

Are you busy and do not have time to handle your assignment? Are you scared that your paper will not make the grade? Do you have responsibilities that may hinder you from turning in your assignment on time? Are you tired and can barely handle your assignment? Are your grades inconsistent?

Whichever your reason is, it is valid! You can get professional academic help from our service at affordable rates. We have a team of professional academic writers who can handle all your assignments.

Why Choose Our Academic Writing Service?

  • Plagiarism free papers
  • Timely delivery
  • Any deadline
  • Skilled, Experienced Native English Writers
  • Subject-relevant academic writer
  • Adherence to paper instructions
  • Ability to tackle bulk assignments
  • Reasonable prices
  • 24/7 Customer Support
  • Get superb grades consistently

Online Academic Help With Different Subjects


Students barely have time to read. We got you! Have your literature essay or book review written without having the hassle of reading the book. You can get your literature paper custom-written for you by our literature specialists.


Do you struggle with finance? No need to torture yourself if finance is not your cup of tea. You can order your finance paper from our academic writing service and get 100% original work from competent finance experts.

Computer science

Computer science is a tough subject. Fortunately, our computer science experts are up to the match. No need to stress and have sleepless nights. Our academic writers will tackle all your computer science assignments and deliver them on time. Let us handle all your python, java, ruby, JavaScript, php , C+ assignments!


While psychology may be an interesting subject, you may lack sufficient time to handle your assignments. Don’t despair; by using our academic writing service, you can be assured of perfect grades. Moreover, your grades will be consistent.


Engineering is quite a demanding subject. Students face a lot of pressure and barely have enough time to do what they love to do. Our academic writing service got you covered! Our engineering specialists follow the paper instructions and ensure timely delivery of the paper.


In the nursing course, you may have difficulties with literature reviews, annotated bibliographies, critical essays, and other assignments. Our nursing assignment writers will offer you professional nursing paper help at low prices.


Truth be told, sociology papers can be quite exhausting. Our academic writing service relieves you of fatigue, pressure, and stress. You can relax and have peace of mind as our academic writers handle your sociology assignment.


We take pride in having some of the best business writers in the industry. Our business writers have a lot of experience in the field. They are reliable, and you can be assured of a high-grade paper. They are able to handle business papers of any subject, length, deadline, and difficulty!


We boast of having some of the most experienced statistics experts in the industry. Our statistics experts have diverse skills, expertise, and knowledge to handle any kind of assignment. They have access to all kinds of software to get your assignment done.


Writing a law essay may prove to be an insurmountable obstacle, especially when you need to know the peculiarities of the legislative framework. Take advantage of our top-notch law specialists and get superb grades and 100% satisfaction.

What discipline/subjects do you deal in?

We have highlighted some of the most popular subjects we handle above. Those are just a tip of the iceberg. We deal in all academic disciplines since our writers are as diverse. They have been drawn from across all disciplines, and orders are assigned to those writers believed to be the best in the field. In a nutshell, there is no task we cannot handle; all you need to do is place your order with us. As long as your instructions are clear, just trust we shall deliver irrespective of the discipline.

Are your writers competent enough to handle my paper?

Our essay writers are graduates with bachelor's, masters, Ph.D., and doctorate degrees in various subjects. The minimum requirement to be an essay writer with our essay writing service is to have a college degree. All our academic writers have a minimum of two years of academic writing. We have a stringent recruitment process to ensure that we get only the most competent essay writers in the industry. We also ensure that the writers are handsomely compensated for their value. The majority of our writers are native English speakers. As such, the fluency of language and grammar is impeccable.

What if I don’t like the paper?

There is a very low likelihood that you won’t like the paper.

Reasons being:

  • When assigning your order, we match the paper’s discipline with the writer’s field/specialization. Since all our writers are graduates, we match the paper’s subject with the field the writer studied. For instance, if it’s a nursing paper, only a nursing graduate and writer will handle it. Furthermore, all our writers have academic writing experience and top-notch research skills.
  • We have a quality assurance that reviews the paper before it gets to you. As such, we ensure that you get a paper that meets the required standard and will most definitely make the grade.

In the event that you don’t like your paper:

  • The writer will revise the paper up to your pleasing. You have unlimited revisions. You simply need to highlight what specifically you don’t like about the paper, and the writer will make the amendments. The paper will be revised until you are satisfied. Revisions are free of charge
  • We will have a different writer write the paper from scratch.
  • Last resort, if the above does not work, we will refund your money.

Will the professor find out I didn’t write the paper myself?

Not at all. All papers are written from scratch. There is no way your tutor or instructor will realize that you did not write the paper yourself. In fact, we recommend using our assignment help services for consistent results.

What if the paper is plagiarized?

We check all papers for plagiarism before we submit them. We use powerful plagiarism checking software such as SafeAssign, LopesWrite, and Turnitin. We also upload the plagiarism report so that you can review it. We understand that plagiarism is academic suicide. We would not take the risk of submitting plagiarized work and jeopardize your academic journey. Furthermore, we do not sell or use prewritten papers, and each paper is written from scratch.

When will I get my paper?

You determine when you get the paper by setting the deadline when placing the order. All papers are delivered within the deadline. We are well aware that we operate in a time-sensitive industry. As such, we have laid out strategies to ensure that the client receives the paper on time and they never miss the deadline. We understand that papers that are submitted late have some points deducted. We do not want you to miss any points due to late submission. We work on beating deadlines by huge margins in order to ensure that you have ample time to review the paper before you submit it.

Will anyone find out that I used your services?

We have a privacy and confidentiality policy that guides our work. We NEVER share any customer information with third parties. Noone will ever know that you used our assignment help services. It’s only between you and us. We are bound by our policies to protect the customer’s identity and information. All your information, such as your names, phone number, email, order information, and so on, are protected. We have robust security systems that ensure that your data is protected. Hacking our systems is close to impossible, and it has never happened.

How our Assignment  Help Service Works

1.      Place an order

You fill all the paper instructions in the order form. Make sure you include all the helpful materials so that our academic writers can deliver the perfect paper. It will also help to eliminate unnecessary revisions.

2.      Pay for the order

Proceed to pay for the paper so that it can be assigned to one of our expert academic writers. The paper subject is matched with the writer’s area of specialization.

3.      Track the progress

You communicate with the writer and know about the progress of the paper. The client can ask the writer for drafts of the paper. The client can upload extra material and include additional instructions from the lecturer. Receive a paper.

4.      Download the paper

The paper is sent to your email and uploaded to your personal account. You also get a plagiarism report attached to your paper.

smile and order essaysmile and order essay PLACE THIS ORDER OR A SIMILAR ORDER WITH US TODAY AND GET A PERFECT SCORE!!!

order custom essay paper