Mean, Median or Mode: A potential employee inquired about the salary paid by a company....

[Mila12]

A potential employee inquired about the salary paid by a company. The interviewer responded with a number that would make salaries at the business sound high, Given the data in the chart, which measure of central tendency did the interviewer use?
Frequency 7 1 3 2 1 1
Salary $15,000. $20,000 $24,000. $70,000 $100,000 $150,000
a) Mean
b) Median
c) Mode
d) Minimum

 

[BigBeachBanana]

A potential employee inquired about the salary paid by a company. The interviewer responded with a number that would make salaries at the business sound high, Given the data in the chart, which measure of central tendency did the interviewer use?
Frequency 7 1 3 2 1 1
Salary $15,000. $20,000 $24,000. $70,000 $100,000 $150,000
a) Mean
b) Median
c) Mode
d) Minimum

I'll get you started. Minimum is not a measure of central tendency. That leaves you with mean, median, or mode.

Can you compute those given the information?
It'll be helpful to draw a histogram to visualize what kind of data we're dealing with i.e. left-skewed, right-skewed, symmetric.

 

[stapel]

A potential employee inquired about the salary paid by a company. The interviewer responded with a number that would make salaries at the business sound high, Given the data in the chart, which measure of central tendency did the interviewer use?

Frequency    7        1        3        2         1         1
 Salary   $15,000  $20,000  $24,000  $70,000  $100,000  $150,000

a) Mean
b) Median
c) Mode
d) Minimum

What have you tried? How far have you gotten? Where are you stuck?

For instance, you found the arithmetic average (that is, the mean). You found the middle of the fifteen values (that is, the median). You noted the most-repeated value (that is, the mode). And you copied down the minimum value.

What were your results? What is your opinion *about* these results?

Please be complete. Thank you!

Eliz.

 

[The Highlander]

A potential employee inquired about the salary paid by a company. The interviewer responded with a number that would make salaries at the business sound high, Given the data in the chart, which measure of central tendency did the interviewer use?
Frequency 7 1 3 2 1 1
Salary $15,000. $20,000 $24,000. $70,000 $100,000 $150,000
a) Mean
b) Median
c) Mode
d) Minimum

Hi @Mila12,

What help do you need?

We won't just give you the answer to this question. That doesn't help you but we will offer you help if tell us exactly what you are struggling with.

The data "given" (a "chart" is mentioned but I don't see one. Were diagram(s) or more information provided that you haven't submitted?) tells me that there are 15 employees in this company (7+1+3+2+1+1=15) and, for example, 7 of them receive a salary of $15,000 (if I am interpreting the "given data" correctly).

On that basis it would be possible to calculate all of the measures of central tendency listed: Mean, Median, Mode & Minimum (although, strictly speaking, the Minimum is not a measure of central tendency).
That would be your starting point (to calculate those four things).

Can you do that?

Please come back and show us your attempt to do so.

If you are not sure how to do that, then please tell us which one(s) you need help with.

We cannot deliver comprehensive lessons on whole topics in a forum like this but are happy to provide help on specific problem areas if members make it clear exactly what help they need.

If you don't know how to calculate any of these things then I suggest you visit a site like this and read up on them, then you can come back and show us your attempt to answer the question whereupon further help/guidance will be offered if necessary.

 

[The Highlander]

Dear @Mila12,

Since this is not an ‘advanced’ topic and you have not given us any idea of what help you might need, I suspect that you are, indeed, someone completely new to the topic of “Statistics” (maybe the 12 in Mila12 is your age?) and you were hoping that we might just give you the answer to the question as you posted it.

As I said previously, that is not what we do in this forum. We are happy to offer help (the clue is in the forum title), not just do the work for new members but, since (I’m guessing) you are new to this topic and haven’t fully understood (or learned) how to work out these “averages” yet, I have put together for you, below, an example that might help you out.

There is no substitute for spending time on studying a subject properly, so I still recommend that you to visit the website I mentioned previously and read through it carefully but my example may help you with not only the question you posted above but also make it easier (and quicker) to learn what is laid out on that site.

Here, then, is an example I have constructed (just for you ?)…

There are fifteen elementary school children living in our street and, as the secretary of the residents’ association, I was asked to present some statistics about our kids to the association’s annual meeting.

I therefore gathered together details about the children’s ages and discovered that there were:-

7 aged 5
3 aged 6
1 aged 7
2 aged 8
1 aged 9
and
 1 aged 10​

I was asked to find the measures of central tendency for the ages of the children in our street so the first thing I did was to put the ages of all the children into ascending order like this:-

5  5  5  5  5  5  5  6  6  6  7  8  8  9  10
​

Now, in order to find the Mode, I needed to know which age came up most often and, clearly, there are more children aged 5 than any other age, therefore, the Mode = 5.
(We would often say: the Modal age is 5 but the Mode = 5 is fine.)

The Median is the value that lies right in the middle of your data (once it has been put into order). We (mathematicians) talk about ‘ordered data’ meaning the numbers have been put into ascending order; ie: lowest to highest. If you look again at my (ordered) data you will see that the number 6 lies right in the middle because there are seven numbers before it and seven after it, therefore the Median = 6.

5  5  5  5  5  5  5  6  6  6  7  8  8  9  10
​

To calculate the Mean for any set of data you need to first count how many pieces of data there are (let’s call that number “n”), then you add up all the data and divide that total by the number there are (n).

Now, rather than adding up all fifteen ages individually, I can find their total (called the ‘Sum’) a little bit quicker by using some multiplication. This approach is particularly helpful if you have to deal with a lot more data than just fifteen.

I know there are 7 children aged 5 so their ages will add up to 7 × 5 (= 35) so I can rewrite my table (from above) like this:-

7 aged 5 → 7 × 5 = 35
3 aged 6 → 3 × 6 = 18
1 aged 7 → 1 × 7 =  7
2 aged 8 → 2 × 8 = 16
1 aged 9 → 1 × 9 =  9
 1 aged 10 → 1 × 10 = 10   
                 95 
​

Can you see how that made my calculation a bit easier? I only had six numbers to add up instead of fifteen! We call this a Frequency Table because it shows how often (bow frequently) each age turned up (occurred).

So I now know the Sum of all my children’s ages (95) and also knew (from the start) how many ages were involved, ie: 15 (which we decided to call “n”) and to find the Mean of any set of data we divide the Sum by “n”, therefore, we need to divide 95 by 15 to find the mean of this data set, thus:-

\(\displaystyle \large\text{Mean}\normalsize=\frac{\text{Sum}}{\text{n}}=\frac{95}{15}=6\tiny\frac{1}{3}\)
​

So the Mean = 6⅓         or 6.333 (to 3 decimal places).

We call this the Arithmetic Mean (because there is another type of mean, called the Geometric Mean, where you multiply all the data together instead of adding them) but when anyone talks about the “mean” then they are almost always referring to the arithmetic mean (unless they specifically say differently) and, also, when people talk about the “average” then, once again, they are referring to the (arithmetic) mean.

In Maths, however, we regard all these statistics (Mean, Median & Mode) as being ‘averages’ or, as they might more properly be referred to, ‘measures of central tendency’.

We call them that because they give us one number that might (quite accurately) “represent” a whole bunch of numbers (because that number lies somewhere near the ‘middle’ of them?).

Now that we have calculated the 'averages' for the ages of the children (Mode = 5; Median = 6 and the Mean = 6⅓) which of those averages do you think best represents the ages of the children in our street? (Mean, Median or Mode?) Please let me know to see if your answer to that question agrees with mine?

As I said previously, the Minimum is not a measure of central tendency' but it's name is fairly self-explanatory, so I expect you can work out what that is without any help from me. (if not, just look it up in any dictionary.)

Hope that helps, Mila. ?