Statistics How To

Welcome to Statistics How To!

Looking for elementary statistics help? You’ve come to the right place. Statistics How To has more than 1,000 articles and hundreds of videos for elementary statistics, probability, AP statistics and advanced statistics topics. Looking for a specific topic? Type it into the search box at the top of the page.

The PROBABILITY AND STATISTICS TOPIC INDEX lists the most popular categories.

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What Does a Statistician Do…Really?

what does a statistician do

What does a statistician do? Not this!

I often get asked the question “What does a statistician do?” and people assume that I crunch numbers. I’ve lost count of the times people have said to me “Oh, I can never balance my checking account.” I patiently explain that number crunching is best left to the accountants. And I’m terrible at balancing my checkbook as well.

The truth is, statistics is less about the numbers themselves and more about the patterns those numbers represent. If you have ever read a Highlights magazine as a kid, then you might remember little logic problems like:
What is the next number in this pattern? 1, 4, 2, 5, 3, 6, 4 (the answer is 7).
Well, statistics is like that but on a much larger scale.

For example, I was recently hired by an e-cigarette company to analyze store data and to try and figure out why some stores weren’t performing as well as others. It was just a logic problem: something was causing some stores to do well, I just had to figure out what that “something” was. I sorted through reams of data (including census data) over several days and found several patterns that probably indicated the success of some stores was due to several factors, including:

  • Proximity to a mall.
  • Lower income in the surrounding areas (lower income earners tend to be smokers at a higher rate than high wage earners).

Multifaceted Roles of a Statistician

The role of a statistician falls into several broad areas:

  • Collect data using statistical techniques like stratified random sampling.
  • Ensure that data is trustworthy.
  • Analyze data to make the meaning clear.
  • Draw conclusions from data.
  • Teach at high school, college, and university.

Statisticians also solve real-world problems in business, science and many other fields. For example, a statistician might work with:

  • Medical research teams to ensure their trials are statistically sound.
  • Environmentalists to look at data for climate change and make predictions about weather patterns based on the data.
  • Businesses, to analyze customer data and uncover buying patterns (i.e. when a customer is more likely to buy a certain product).

How to Become a Statistician

A master’s degree is usually required to begin a career in statistics. It doesn’t have to be in statistics, although you’ll probably need some kind of math. My masters degree is in mathematics education, and I started teaching college statistics (and building this site!) right after graduation. Statisticians earn reasonable money, but it’s not going to make you rich: according to the Bureau of Labor and Statistics, the median pay for 2012 was $75,560 per year.

Statistics How To Recommends these other sites!

Welcome to Statistics How To! was last modified: April 9th, 2017 by Stephanie

122 thoughts on “Welcome to Statistics How To!

  1. Benedikt Björnsson

    Hi Stephanie!
    I´m studying at Agricultural Universiti of Iceland at Hvanneyri.
    This morning I payed for your book and I´m out of words about it.
    How com, it is possible to listen to lectures at an university, without getting the whole picture of a subject and by reading your explanation in few words and then all of a sudden, get the compleate picture?
    By using your words introducing your book, “students who use it never fail, and their average grade is one or two letter grades higher than other students”.
    That look logical to me, “You must be a good teacher by nature!”
    Thanks for your effort!

  2. Andale


    Thank you so much for saying this. I’m really glad it helped :)

    Good luck with your studies!


  3. Carlo

    Great blog. I had some problems dealing with normal distribution on excel and thanks to your guide I solved it easily.

  4. Anita

    I am considering buying your book, but from the pre-view it doesn’t seem to assist with interpreting results from SPSS or to assist with interpreting results from descriptive statistics in general. I am struggling with the basics (as you can see) and need to interpret results for “Business Research” as a subject not so much only statistics. Our curriculum includes quantitative- and qualitative research, although my request to you pertains quantitative interpretation.

    Will this book cover interpretation of statistics as well?

  5. Andale


    SPSS interpretation isn’t in the book…it covers the basics for an elementary stats class and most elementary stats classes don’t use SPSS. That said, you can find some SPSS articles here.

    Also, if you get stuck on something, feel free to post a comment and I’ll see if I can tackle it for an article.


  6. Giovanni Blancas

    Hi, how can I register for your forums? I don’t see register link on your site. I am trying to help my son with his science project which requires some statistical analysis. Thanks.

  7. Andale

    Hi, Giovanni,

    The board was temporarily closed to registrations. Registrations are now up: please click the “Register” button next to Login/FAQ.

    Thanks for stopping by :)

  8. Frezi


    Is elementary statistics the same as a basic college Introductory Statistics course? I’m actually using this to help with studying for Finals.


  9. Steve Hyatt

    Stephanie, I am not a math-major. 2nd, it has been 35 yrs or so since I have taken and high school or college math/algebra. No Calculus or Trig taken at all in past. My college path now requires a basic introduction to STATS and for some reason I took it online with my instructor being in California and me being in central US. Book is online as well. My problem is the book doesn’t give enough explicit detail on how to complete a statement. I will go as far as to state the book doesn’t even give a bottom line definition for a mean or what the parts are of the statement presenting a normal distribution. Here I am and in chapter 7 and next week is final time. Just by hook or crook I recalled what the “alpha” symbol is/was but did not recall how to compute anything about it. Can you help? Thank you! …..Steve

  10. el_farouq

    I came across your website and I find it interesting and understanding to be able to solve statistical problems. I have a question here on baye’s theorem.

    1- A manufacturing company employes three analytical plan for the design and development of a particular product. For cost reason, all three are made at varying time. Intact, plan 1, 2, 3 are used 30%, 20%, & 50% of the product respectively. The perfect rate for the three plans are 0.01, 0.03, 0.02 respectively. If a random product was observed and found to be defective, which plan, was must likely used and thus, responsible.

    2-Police plan to enforce speed limit by using radar trap at four different locations within city limit. The radar trap at each of the locations are 40%, 30%, 20%, and 30% of the time respectively. If a person who is speeding on his way to work has probability of 0.2, 0.1, 0.5, and 0.2 respectively, of passing this locations, what is the probability that he will receive a speeding ticket?

  11. Andale

    Hello, El Farouq,
    Unfortunately I don’t have the time to answer stats question in comments, but if you would like to post on our forum, one of our mods will be glad to help!

    P.S. Make sure you tell them what you know/have tried :)

  12. onesmus

    Can anyone give me the answer?
    What is sampling? Give a definition and then go on to describe situations that necessitate sampling to be conducted

  13. onesmus

    reply to my email: [email protected]

  14. Hanna

    Hi Stephanie,

    I’m considering buying your handbook. So far it looks helpful, however I couldn’t find the stats/List Editor under APPS. Will you have more calculator help in the handbook?

  15. Andale

    Hello, Hanna,
    I’m updating the TI89 manual with instructions on how to get the app. It’s a TI program and you can download it here:

    The e-version of the handbook comes with a TI89 guide.
    Best of luck with your course!

  16. Todd Marshall

    A table in the back of the book references this broken link. It troubles me that tables are not included in the download. Broken links like that that will make the book less valuable in time as links are moved and abandoned. Further, it means I can’t use the book absent the internet. This content should be included in the download.

    The book itself is not what I had hoped for. However, the price (one night at the honky tonk drinking beer) is worth the risk and I’m hoping there’s some useful content.

    A book that would be valuable to me would be one that decodes the myriads of notation found in math and statistics. For example, the integral sign means “find the area under a curve” for the limits given at the top and bottom of the sign. Pretty simple concept, but believe it or not I went through introductory calculus twice before I realized (it was never specifically told to me) that integration was finding an area.

    When you start talking about Hamiltonians and Hermetians things get totally out of hand.

  17. Andale

    Thanks, Todd. I will get to work fixing the broken link. In the meantime, it’s redirecting to the correct page. I can see how a book on the notation would be useful but whew…what a huge endeavor that would be! I have added a couple hundred articles to this site on definitions and I have tried to define statistics terms in plain English. I hope you find the site content to be a helpful addition to the book. Regards, S.

  18. fran

    Hi your permutation calculator is not working as it does not generate the distribution when you enter data set. Please see to it. Fran 20 Apr, 2015

    Please remove my previous comment no 27.

  19. heidi

    Hi Stephanie,

    Thanks so much for this site!! It’s helping drastically with an online stats course I’m doing!! Keep up the good work and thanks again!!

  20. Daniel Buller

    How do you find the new mean and standard deviation if your data was off by 1. Such as weight. If your mean is 180.29 and your standard deviation is 10.36 with 100 people, but no data set

  21. Salote

    Hi Stephanie thanks a bunch for this website it is of great assistance with my online course I am currently pursuing.


  22. Mohammed Adnan Suleman


    I’m currently undertaking a forecast comparison on two aircraft manufacturers and would like to know what tests would be ideal to use if i wish to compare the two together? Chi square, T test or paired T test? Look forward to hearing from you.


  23. Mo


    Sorry which table, all I’d like to do is compare the two aircraft manufacturers forecasts in terms of economic, passenger air travel demand and freight market.


  24. nick Schneider

    I purchased the downloads for practical cheating for 19.93 via PayPal but do not have the site to download the items. Where can I get my downloads?

  25. Quinton

    Helping my daughter with science fair project. We are using spirometry data from my clinic to see which gender smoking ages the lungs the most. My daughter thinks smoking ages a woman’s lungs the most. However, wouldn’t the null hypothesis be there is no gender difference in lung age?

    To come up with how much smoking has aged the lungs we subtract the spirometric lung age from biological age. We get this table listed below. We kinda sorta after cutting and pasting. The first roll is the females and the second roll is males.
    Female Years Lung Aged Male Years Lung Aged
    37 33
    30 1
    25 29
    26 0
    23 0
    28 12
    26 25
    37 40
    38 0
    20 36
    27 21
    27 12
    46 42
    41 19
    20 37
    33 1
    8 21
    23 2
    36 16
    26 18
    12 19
    13 21
    4 5
    41 13
    25 13
    60 39
    Doing the F test as I followed you on YouTube I get this…
    F-Test Two-Sample for Variances

    Male Years Lung Aged Female Years Lung Aged
    Mean 18.26923077 28.15384615
    Variance 188.3646154 148.2953846
    Observations 26 26
    df 25 25
    F 1.270198772
    P(F F I can’t reject the null? I guess I need to basically say, there is no significant differences in aged lungs from smoking between the two groups.

    Thanks for your help.

  26. Quinton


    When I ran a t test it looks like I can reject the null. How can I determine which to use, t or F testing?
    t-Test: Two-Sample Assuming Unequal Variances

    Female Years Lung Aged Male Years Lung Aged
    Mean 28.15384615 18.26923077
    Variance 148.2953846 188.3646154
    Observations 26 26
    Hypothesized Mean Difference 0
    df 49
    t Stat 2.746949591
    P(T<=t) one-tail 0.004196
    t Critical one-tail 1.676550893
    P(T<=t) two-tail 0.008392
    t Critical two-tail 2.009575237

    Thanks again.

  27. Andale


    It sounds like you have two samples, and you think one ages more quickly than the other. Therefore, your null would be:
    H0: no difference
    H1: there IS a difference

    The F test looks for a difference in variances. The results from the f test here would be “there is no significant differences in the VARIANCES in aged lungs from smoking between the two groups”.

    I think you probably want to run a t test for a difference in MEANS. T Test for Independent Samples

    If you really did intend to run a test for variances, then compare the f-value from the test to your f critical value. Your test results state the F critical value is F 1.270198772, but I don’t know what your test F value is. If the f-value is higher, you can generally reject the null (that the variances are equal).

  28. Andale

    You would use a t to test for differences between means and the f to test for a difference in variances.

  29. Sally

    Thank you very much for this site! Extremely helpful. I was reading the page “Sample Variance in Statistics: What is it?” and it helped a great deal to get my head around how variance actually fits in. There was one curious point where is covers the mean of 150 minus the variance of 99. Shouldn’t this be 51? It says 151 on the page.

  30. Brandon Morden

    Hi Stephanie,
    I am a Canadian who is desperate need of help for some of my stats assignments. If you could explain this question to me and the steps in finding the answer that would be a big help come test time.
    The mean amount purchased by each customer at Churchill’s Grocery Store is $25 with a standard deviation of $9. The population is positively skewed. For a sample of 41 customers, answer the following questions:

    a: What is the likelihood the sample mean is at least $29? (Round the z-value to 2 decimal places and the final answer to 4 decimal places.

    b: What is the likelihood the sample mean is greater than $23 but less than $29? (Round the z-value to 2 decimal places and the final answer to 4 decimal places.)

    c: Within what limits will 98% of the sample means occur? (Round the final answers to 2 decimal places.)

    All three questions are asking for sample mean
    Thanks for you help


  31. Austin

    Im having trouble with this one problem. It states find the critical value and give me an n=60 and, a=.05. I’ve looked at the youtube videos and I know how to get a critical value but I cannot figure out this problem. Every critical value I have found does not give me one of the choices. +-.255,+-.253,.255, 0r -.255

  32. Andale

    Can you post the full question? I need some more info to fully answer your question. n=60 and a=0.05…is this for a t-critical value?

  33. Jackie Mark

    I am in a research course and we have reached the statistics portion of the class with minimal instruction on how to do it. I am attempting to discover if there is a correlation maybe? between the responses I receive and the gender or location of a respoder. I have put the information into an excel file and then discovered that I have absolutely no idea what I’m supposed to do with it. The responses have been coded as have the location and gender, I just don’t know how to get the information I need I guess. Is there any information you could give me as to what method I should use to gather this information from my file? Anything would be appreciated. I could analyze based on your videos I’m sure, but first I need some idea of what kind of statistics method I should use for the data analysis.

  34. marwan salah salman

    Dear friend
    Thanks alot for these worthy information , i am ophthalmologist and doing research and doing statistical analysis and p value but iam not sure about it, can send figure to you to be sure the p value is correct

    thanks alot

    clinical assisstant professor dr. marwan salah salman

  35. Andale

    If you’d like to post some info about what your p-value calculations are, I’d be happy to check it.

  36. Rory

    Grocery shopping question

    Hi Gang, could someone please point me in the right direction. I need to set up an excel spreadsheet that will show me the number of possible grocery combinations. There are 200 grocery items from 7 categories (meats, vegetables, etc.), each item has a unique monetary value, you can only use each item only once per combination, and you only have $500 to spend.

    Furthermore, there are 7 grocery categories which must be filled with a specific number of items ( 2 meats, 3 vegetables, 1 desert, 1 bread, 1 juice, etc).

    How can I get all the possible results!!?? Please help.

  37. Sekeli Maboshe

    When selecting the level of significance alpha, what factors do i have to consinder that can affecte the choice of level of significance?

  38. Andale

    I’d say mostly what confidence level you are willing to accept. A 1% alpha level (99% CL) is going to be way more precise than a 10% alpha level (90% CL).

  39. diamond doctor dallas

    It’s very simple to find out any matter on net as compared to textbooks, as I found this
    post at this site.

  40. Prasit Rattanasupa

    Dear sir/madam:

    The local educational agency had notify the teachers to calculate the average T score of the their scores before and after learning. May I ask your utmost advice if it is possible to evaluate the Z score and T score using the steps below. But I can not typing formula on this. Can I sent it by my e_mail.
    Your kind thought is highly sought.
    Thank you very much.
    Sincerely yours,
    Mr. Prasit Rattanasupa

  41. Andale

    I do offer statistics consulting services, but if it’s a quick question I may be able to help without charge. My email is [email protected].

  42. Melissa

    Hello, I watched a video of yours on how to plot a histogram on the Ti-89. I am still unsure how to do it, as I have two sets of data, the mid-point (for the x values) and the frequencies (for the y values). I’m not sure how to enter it in the ‘Plot 1’ Section, as it only allows me to enter the first column of information and not the second. Any help would be appreciated. Thank you.

  43. Jack Weakley

    I placed an order for your book download, and I want to cancel that order. I didn’t download the book

  44. Ayo

    This is quite an interesting lesson. Please what is the sample size of population size of 300? How do I go about the calculation?

  45. sarinee

    very interesting you tube presentation, grateful if you could help in steps in traditional and p-value of hypothesis testing

  46. Vanshika Datta

    Will you please tell me how to become an actuary after doing bsc maths honours and what does he do.

  47. Francisco

    Good Nigth!
    How can to find standard score z from probability in normal standard?

  48. Andale

    Hello, Earles, if you buy the ebook here I’ll ship you a paperback copy of the PC book. Just make sure to include your address in a note if you pay by paypal :)

  49. ayodele


    Please, what is the dependent and independent variable for this research topic “knowledge and determinants of substance use and abuse among people living with special needs in ibadan.
    Hope to hear from you soon. Thank you for reply in advance

  50. Andale

    The independent variable is constant (i.e. it doesn’t change) so I would say the people living with special needs is the independent variable. So substance abuse would be the dependent.

  51. Chris

    Hi, I’m applying for a post as an Assistant Statistician in Northern Ireland. Part of that application involves being tested on “basic statistical and social research concepts”. It’s been 6 years since I graduated with a Psychology degree ans (sadly) most of my statistics knowledge has evaporated. Is there a resource on this site that might prove helpful?

    Thanks in advance

  52. Leaders

    Hi. I intend to do my undergrad research on Occupational Safety and Health among farm workers, focusing on factors affecting safety and health practices on the farm. Could you give me some pointers on the study design, variables, and data analysis methods?

  53. Andale

    Hi, Leaders, I’m afraid OSHA and farm workers is outside of my area of expertise, so I wouldn’t know where to begin with a study design or variables. Data analysis methods are pretty standard across the board, but it would depend on what your goals are — i.e. identifying specific factors, finding means, comparing means etc. What exactly is your research hypothesis? I would start there.

  54. sarah

    Hi, would you pleas add section about types of comparison in clinical trials life non inferiority study design,what is the def. of the non inferiority margin and how it is determined?

  55. Jeff


    Thx for taking the time to create this site and the wonderful and very informative videos as they have helped me immensely.

    I had a quick question on moving averages. Say I have a data set of 120 days and I would like to see the average of emails sent per user. I assume a moving average would be the way to go to help smooth out any peaks/valleys that a shorter time might indicate.

    Would sampling a certain amount of days provide some “smoothing”, or is it best to run the search for the average on the entire dataset?


  56. Andale

    If you suspect there’s a trend going on, a moving average of a certain amount of days will reveal it. That said, it doesn’t sound like you are looking for a trend, or suspect there’s a trend, so I’m not sure what use a MA will do for you. I would run a regular old average on the whole set.

  57. Bess

    I am a first-year university student that is struggling with statistics and I just wanted to let you know that your website has been a lifesaver!

    Thank you!

  58. Paul

    I am a graduate student at university. I want to analyze the training effect on firm performance,
    To analyze this particular question, I want to use propensity score matching method.
    But I don’t know how I should analyze my research question with propensity score matching method.
    I would appreciate any recommendation or feedback. Thank you in advance.

  59. Delores

    I’m stupid with this statistics. Here is the problem. Past records indicate that the probability of online retail orders that turn out to be fraudulent is 0.08. suppose that, on a given day, 20 online retail orders are placed. Assume that the number of online retail orders that turn out to be fraudulent is distributed as a binomial random variable. (a) what are the mean and standard deviation of the number of online retail orders that turn out to be fraudulent? (b) what is the probability that one online retail order will turn out to be fraudulent? (c)what is the probability that one online retail order will turn out to be fraudulent?
    (d) What is the probability that two or more online retail orders will turn out to be fraudulent?

  60. Rose Goehring

    I am wondering how many combinations of 7 letters can make 5 letter and 6 letter words. A letter may or may not be repeated in the sequence of 7 letters, but only those 7 letters “exist”.
    How do you calculate this? I do not know statistics.

  61. Andale

    Have you tried the combinations calculator? You’ll want to put in 7 for “r” then 5 for “n”. Repeat for “n” as 6. Try the generator at the bottom of the page also. Most of the words will be nonsensical (just random letter combinations).

  62. Sian Williams

    Dear Sir / Madam,

    WJEC ( is an awarding organisation that provides assessment, training and educational resources in Wales and England.

    The resources provided by WJEC to support teachers and students often include material from a wide variety of sources. The use of this original material increases the validity and relevance of the resources making them more interesting and attractive.

    WJEC are currently developing a guide to support the teaching of Geology and would like to gain copyright permission to include the ‘Small standard deviation’ and ‘Large standard deviation’ images found on your site.

    The Guidance for Teaching will be freely available on our website ( / and appropriate acknowledgement will of course be made.

    WJEC is a charity and, as such, its role and resources are very different from a commercial publishing company. If you are likely to make a charge for your material, we would be grateful if you would take into account our status as a charity and the use of the material in the context of an educational service.

    I hope we have provided sufficient information and that copyright approval will be granted. If you do not control the rights of the above work but are aware of the copyright holder, then we would appreciate receiving any information that can direct us to the source.

    Thank you and I look forward to your response,

  63. Andale

    Yes, that’s not a problem at all. Please link back to this site. Thanks, and good luck with your project!

  64. Satin Youth

    It’s nearly impossible to find well-informed people for this
    subject, but you sound like you know what you’re talking about!

  65. Chris

    Can you recommend a good book to learn from before signing up for a class ? Trying to get a head start

  66. Armani

    Just wanted to drop a line and say thanks! Came across this site from a google search working on a take-home stats midterm (PhD student). Then came across it again later while working on another problem. Both times it was the MOST helpful site. Awesome site! Much appreciated!

  67. Paul Sherwin

    HI, in the article, “Sampling With Replacement / Sampling Without Replacement”, there is an error. Under sampling without replacement, the outcome “John,John” is listed as a possibility. Since sampling is without replacement and there is only one instance of “John” in the hat. it is impossible for “John” to be drawn more than once.

  68. Andale

    Chris, you could start with the basic statistics section on this site. It’s free ;)
    As far as a book: If it was me, I would purchase the textbook for my class in advance and work from that.

  69. Meticularius

    I’m a 69 year old Grandfather who left behind the study of statistics in 1986. I appreciate your work here. It has reopened my mind to what I left behind, and brought new (and I think better) meaning. A younger friend is having difficulty and I have recommended your work here to her.

  70. Jason Sandusky

    I am in a Java writing class and I am trying to figure out the Java code to do the combination generator like you have on your site. Is it possible for you to send me a copy of that code?

  71. Amish Gupta

    Your site is the best that I’ve ever came across in every aspect of what a student aspires.
    The language is so easy, not many jargons were used and if used, consisted of a hyperlink. The explanation is accurate and brief. The site had all the topics that I needed to study for my subject (Econometrics).
    Keep it up!

  72. Vikram Kumar

    Dear Sir

    I am the scholar and working in the field of Hydrology and often have to work for statistical calculation. May I know do you have Matlab code to calculate the common statistical parameters. If then can you please share it with me.

  73. Lerato

    Can you please help me come up with a bin range so I can draw my histogram using excel. The data is 23571,23988,25871,22608,23953,24855,28511,26730

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