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- Descriptive Statistics.
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- Critical Values, Z-Tables and Hypothesis Testing.
- Sampling and Finding Sample Sizes.
- Chi Square.
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- Microsoft Excel for Statistics.
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## What Does a Statistician Do…Really?

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!

- Algebra's Friend.
- Math as a Second Language.
- Mathematical Mischief.
- Mathematics and Multimedia.
- She Loves Math.
- Simplifying Radicals.
- White Group Mathematics.
- Wild About Math.
- Mathematics Simplified.
- Mathematics SI.

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!

Benedikt

Benedikt,

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

Good luck with your studies!

Stephanie

Can you help me with missing data?

Emmanuel,

You may have some luck posting on our forums.

Stephanie

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

Thanks

Carlo

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?

Anita,

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.

Regards,

Stephanie

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.

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 :)

u r doing a nice job here. Keep it going

Thank you!

Hi,

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

Thanks!

Yes, it’s exactly the same :)

what is a 5 number summary

The five number summary explained

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

Does this help? What is an alpha level?

Hello,

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?

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 :)

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

reply to my email: [email protected]

Hello, Omesmus,

If you post on our forum, one of our mods will be happy to help!

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?

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!

Stephanie

http://www.statisticshowto.com/tables/chi-squared-distribution-%20table-right-tail/?PageSpeed=noscript

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.

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.

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.

Thanks for letting me know! We’re working on a fix right now.

I have registered but can’t access forum to post?

What error message are you getting?

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!!

Heidi

Glad it’s helping! Good luck with your class :)

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

Hi, Daniel,

I’m not sure what you mean by “your data was off by 1”. Please post on our help forum and one of our mods will be happy to help :)

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

:).

Please continue with more Exercises

Hi

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.

Mo

It depends on what kinds of variables you have. This table may help.

Hi

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.

Mo

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?

Hi, Nick,

You should have the email with the downloads. If not, please let me know!

Stephanie

Lots of information on statistics can be found on this website. Good work!

I see the videos. All i can say is Love you

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.

Quinton

Hello

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.

Quinton

Quinton,

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).

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

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.

Hi, Sally. Thanks for catching that typo. It should be 51 (now fixed!).

This is really helpful.

Thanks a lot Friend ☺

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.

Question

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

Brandon

Check out the normal distributions word problems page. That should walk you through the steps for questions like these.

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

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?

You’re an extremely practical site; couldn’t make it without ya!

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.

You need to choose a nonparametric test. You’ve got several options. Try the logistic or Kendall’s Tau.