Quoted Text

Kohli said Schenectady’s weekly wage average is above the national average because of the presence of 5,600 high-paying manufacturing jobs in the county. “These are jobs that are paying an average of $1,500 a week, and that brings up the county average,” he said.

Mean, Median, Mode, and Range

Mean, median, and mode are three kinds of "averages". There are many "averages" in statistics, but these are, I think, the three most common, and are certainly the three you are most likely to encounter in your pre-statistics courses, if the topic comes up at all.

The "mean" is the "average" you're used to, where you add up all the numbers and then divide by the number of numbers. The "median" is the "middle" value in the list of numbers. To find the median, your numbers have to be listed in numerical order, so you may have to rewrite your list first. The "mode" is the value that occurs most often. If no number is repeated, then there is no mode for the list.

The "range" is just the difference between the largest and smallest values.

Find the mean, median, mode, and range for the following list of values:
13, 18, 13, 14, 13, 16, 14, 21, 13

The mean is the usual average, so:

(13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13) ÷ 9 = 15

Note that the mean isn't a value from the original list. This is a common result. You should not assume that your mean will be one of your original numbers.

The median is the middle value, so I'll have to rewrite the list in order:

13, 13, 13, 13, 14, 14, 16, 18, 21

There are nine numbers in the list, so the middle one will be the (9 + 1) ÷ 2 = 10 ÷ 2 = 5th number:

13, 13, 13, 13, 14, 14, 16, 18, 21

So the median is 14.   Copyright © Elizabeth Stapel 2004-2011 All Rights Reserved

The mode is the number that is repeated more often than any other, so 13 is the mode.

The largest value in the list is 21, and the smallest is 13, so the range is 21 – 13 = 8.

mean: 15
median: 14
mode: 13
range: 8

Note: The formula for the place to find the median is "( [the number of data points] + 1) ÷ 2", but you don't have to use this formula. You can just count in from both ends of the list until you meet in the middle, if you prefer. Either way will work.

Find the mean, median, mode, and range for the following list of values:
1, 2, 4, 7

The mean is the usual average: (1 + 2 + 4 + 7) ÷ 4 = 14 ÷ 4 = 3.5

The median is the middle number. In this example, the numbers are already listed in numerical order, so I don't have to rewrite the list. But there is no "middle" number, because there are an even number of numbers. In this case, the median is the mean (the usual average) of the middle two values: (2 + 4) ÷ 2 = 6 ÷ 2 = 3

The mode is the number that is repeated most often, but all the numbers appear only once. Then there is no mode.

The largest value is 7, the smallest is 1, and their difference is 6, so the range is 6.

mean: 3.5
median: 3
mode: none
range: 6

The list values were whole numbers, but the mean was a decimal value. Getting a decimal value for the mean (or for the median, if you have an even number of data points) is perfectly okay; don't round your answers to try to match the format of the other numbers.

Find the mean, median, mode, and range for the following list of values:
8, 9, 10, 10, 10, 11, 11, 11, 12, 13

The mean is the usual average:

(8 + 9 + 10 + 10 + 10 + 11 + 11 + 11 + 12 + 13) ÷ 10 = 105 ÷ 10 = 10.5

The median is the middle value. In a list of ten values, that will be the (10 + 1) ÷ 2 = 5.5th value; that is, I'll need to average the fifth and sixth numbers to find the median:

(10 + 11) ÷ 2 = 21 ÷ 2 = 10.5

The mode is the number repeated most often. This list has two values that are repeated three times.

The largest value is 13 and the smallest is 8, so the range is 13 – 8 = 5.

mean: 10.5
median: 10.5
modes: 10 and 11
range: 5

While unusual, it can happen that two of the averages (the mean and the median, in this case) will have the same value.

Note: Depending on your text or your instructor, the above data set may be viewed as having no mode (rather than two modes), since no single solitary number was repeated more often than any other. I've seen books that go either way; there doesn't seem to be a consensus on the "right" definition of "mode" in the above case. So if you're not certain how you should answer the "mode" part of the above example, ask your instructor before the next test.

About the only hard part of finding the mean, median, and mode is keeping straight which "average" is which. Just remember the following:

mean: regular meaning of "average"
median: middle value
mode: most often

(In the above, I've used the term "average" rather casually. The technical definition of "average" is the arithmetic mean: adding up the values and then dividing by the number of values. Since you're probably more familiar with the concept of "average" than with "measure of central tendency", I used the more comfortable term.)


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A student has gotten the following grades on his tests: 87, 95, 76, and 88. He wants an 85 or better overall. What is the minimum grade he must get on the last test in order to achieve that average?
The unknown score is "x". Then the desired average is:

(87 + 95 + 76 + 88 + x) ÷ 5 = 85

Multiplying through by 5 and simplifying, I get:

87 + 95 + 76 + 88 + x = 425
                      346 + x = 425
                                x = 79

He needs to get at least a 79 on the last test.

Quoted Text

BY MICHAEL LAMENDOLA Gazette Reporter

Poor, poor Lamendola.  I guess it's good that they allowed him to report on something in the city again.  I mean, after talking to someone tonight, I heard that he has been pushed out of the county and is doing most of his work up towards Amsterico nowadays.  He's got the Montgomery County beat now.

Quoted from TakingItBack

What I see in the article clear as day is that Schenectady is not currently capitalizing on one of the greatest potentials in the whole country which is to grow manufacturing and distribution.  The United States is undergoing an unprecidented growth in manufacturing jobs again due to the weak dollar and we are replacing the most prime parcel of land at Alco to build more residential units.  It does not make any sense.  How are we rewarding GE for staying.  How are we rewarding STS Steel by landlocking them.  

That makes perfect sense.  

Don't  worry about STS Steel I'm sure they are just waiting for the most oppurtune time to relocate via a sweetheart deal from the Plex.   Either from the Condo project will be such a success that they need their land to expand or Condo sales will lag due to the existence of a steel plant in your backyard.   Not to mention the RPI "nuclear" facility which at last report was to cost around $500,000.00 to move out of there.   The Mayor for Sch'dy stated a few months ago in the Gazette that he felt RPI should pay for it's removal.   May seem unlikely as they are having their own endowment issues.  Again, who in their right mind would want to live in between these 2 most definite eyesores.   Watch for it.

Quoted from bumblethru

UNPRECIDENTED??? REALLY? Where? And what is it that we are manufacturing in this country.....other than printing money faster than we can spend it and pay it back?

About 2 weeks ago I was tuned in to C-SPAN and listening to a respected economist from one of the think tanks in Wash. DC.   He stated that we have only replaced 300,000 of the the 2.3 million manufacturing jobs lost since before the Great Recession (or the little Depression).   We would need by his calculations 2 million more just to break even.   For 2 more slants on this I refer you to the front page of the local Times-Union for 2/3/12 titled "No Jobs Rebound".  Briefly the article states that the area lost16,700 jobs since 2008.   Comptroller De Napoli states that our area was one of a handfull of regions to have posted net job LOSSES in 2010 and 2011, where most other areas of the state posted modest emploment GAINS.   The piece goes on to further state that the average pay for the jobs that were created in the past 2 years is more than 40 PERCENT LOWER than those lost in the recession.   Also if anyone has access to the NY POST of 2/4/2012, page 21, you will see an article citing how the Fed. Gov't manipulated the "creation" of those 243,000 jobs report for Jan, 2012.   Basically the math equation was thus.   The Gov't expected a higher amt. of job losses for 1/12 and since it was less that the higher number the difference was stated as job creation.   It's like if you said 300 people were to be laid off and in actuality only 200 were, you have "created" 100 jobs.   Read more at john.crudele@nypost.com

Am sure the waiters/waitresses,paking lot attend.,ticket taker at Bowtie and theretail clerks are more than happy reading of the average wage fortune that exists.       Your average wage WOULD have to be alomst this high to pay your tax bills for living in Sch'dy County.

An attempt to demystify the psychlogy of is it or isn't it so.   1)The US economy is a consumer driven economy.   70% of it is consumer driven.   2)As of now people are cautious, not spending enough to drive the economy, hence the stagnation.    3)Solution.    Start talking up improvements in the economy with the latest "report" whether 100% factual or not.    Continue with the rhetotic  voiced by those Gov't officials/Wallstreeters offering up the all is well tune.   4)Whether it's a truth or lie if you here it enough you begin to become convinced, if ever so gradually.   5)You loosen your wallet and begin to spend.   Others follow suit.   The snowball effect of a flood of $$$$$ into the stagnant economy makes what wasn't so,so.   Recession over.   It's all in the psychlogy.

Quoted from Mr. Majestyk

An attempt to demystify the psychlogy of is it or isn't it so.   1)The US economy is a consumer driven economy.   70% of it is consumer driven.   2)As of now people are cautious, not spending enough to drive the economy, hence the stagnation.    3)Solution.    Start talking up improvements in the economy with the latest "report" whether 100% factual or not.    Continue with the rhetotic  voiced by those Gov't officials/Wallstreeters offering up the all is well tune.   4)Whether it's a truth or lie if you here it enough you begin to become convinced, if ever so gradually.   5)You loosen your wallet and begin to spend.   Others follow suit.   The snowball effect of a flood of $$$$$ into the stagnant economy makes what wasn't so,so.   Recession over.   It's all in the psychlogy.

The problem is with the psychology of the foreign nations that buy our debt.  They know our economy is 70% consumption.  We do not produce, we do not save, and the dollar is propped up by debt.  Nations like China know this.  How long will China buy our debt at nearly zero percent interest rates?  Eventually we will have to raise interest rates to attract lenders to buy our national debt.  Once that happens, the dominoes will begin to fall.  The days of cheap money will be gone; the days of funding our government on a credit card will be over.  The bureaucracy will be too large for a consumer based society to maintain.  We borrow 40 cents on every dollar to spend on government programs...Right now we pay it back at a very low interest rate...If the interest rate on the 40 cent per dollar goes up - who pays?  Where does the money come from?  Print more?  That just devalues EVERYBODY'S money.  How long will China allow us to pay them back with a devalued dollar?  

Production has value.  Consumerism does not create value or wealth.  America is a giant flea market where other nations dump their goods.  As long as the U.S. dollar is the world reserve currency we can get away with it.  

I hope people don't believe just spending their savings or spending on credit ends the recession.  That is what created this problem.  People need to look at U.S. economic policy and prepare for the rising interest rates and save accordingly.  Don't let the bankers convince you otherwise...They are the ones that become wealthy providing the consumer cheap money keeping you on the hampster wheel of perpetual debt.

Quoted from CICERO

We do not produce,    (Yadda yadda yadda)
Production has value.  Consumerism does not create value or wealth.  America is a giant flea market where other nations dump their goods.  

US Manufacturing Output vs. Other Countries

US Manufacturing is almost back to 2006 output levels and close to 2006 labor costs while countries like Canada,
Italy, Germany, Japan and the UK’s output levels have declined and labor costs have increased.
Canada, Italy, Japan and Italy’s manufacturing output is down 10-15% from 2006, while Germany’s manufacturing
output is down around 5 %.  Also, labor costs have increased around 10% for these countries since 2006.

This contrasts with the US Manufacturing output being around the same level of 2006 and decreased labor costs
versus 2006 labor costs.

Look at debt to GDP.  Our manufacturing output levels aren't enough to support the current federal bureaucracy.  That isn't factoring in state debt.  Our federal debt is closing in on 100% of GDP.  We are not producing enough to pay for our government.  Who care about our production levels against 5 selected nations.  Let's look at our national spending levels against those nations.  Compare household savings rates and household debt.  America doesn't only have a national debt crisis, we have a personal debt crisis.  

Quoted from CICERO

Look at debt to GDP.  

Yup!  Thank God Obama has managed to get US Manufacturing back to it's 2006 level... where it was before Bush drove
the economy over the cliff...
or those numbers would be much worse.

So does this mean the need for welfare has gone down? Is there less than 60% on welfare now? How many folks are now off of welfare and are now working in these new jobs?

That is the real plumb line!

Can't have it both ways but they do.

Quoted from Box A Rox

Yup!  Thank God Obama has managed to get US Manufacturing back to it's 2006 level... where it was before Bush drove the economy over the cliff...or those numbers would be much worse.

Thank God Obama drove down the value of the dollar by creating more debt making it affordable for other nations to buy U.S. manufactured goods.  Now if he can just collapse the dollar, things will be great!!!  Americans won't be able to buy the goods they make, but hey, foreigners can.

No matter what the nayboobs say -- the FACTS speak for themselves Schenectady County has the highest wages in the area and we are growing jobs.  

THE RENAISSANCE CONTINUES !!!!!!

Quoted from DemocraticVoiceOfReason

No matter what the nayboobs say -- the FACTS speak for themselves Schenectady County has the highest wages in the area and we are growing jobs.  

THE RENAISSANCE CONTINUES !!!!!!

Yep, the FACTS speek for themselves,  The wages in Schnectady are going DOWN.  
Yep, the FACTS speek for themselves   Wages elsewhere, particularly Saratoga are going UP!  
Yep, the FACTS speek for themselves.   Saratoga is gaining MORE JOBS then Schenectady.
Yep, the FACTS speek for themselves.   Property values in Schenectady are going DOWN DOWN DOWN
Yep, the FACTS speek for themselves.   Property values in Saratoga are going UP UP UP.
Yep, the FACTS speek for themselves.   Houses are NOT selling in Schenectady, people do NOT want to live in the city
Yep, the FACTS speek for themselves    Saratoga sees no problem selling houses
Yep, the FACTS speek for themselves    Taxes in Schenectady are almost the highest in the country.
Yep, the FACTS speek for themselves.   In Schenectdy, the poor homeonwers pay the property taxes of the rich


Care to dispute these facts, DV?????    And provide some proof?????    Huh?