Wording

[Maths!!!!!]

Hay all, just started re-studying after 15 years, was looking for some clarity in wording/ (This is part of my question) Use these two values to calculate the average (mean) rate of change of ice coverage per year over this period.

The word mean threw me, do I find the mean of the two values, then the rate of change, or simply just take away both values and proceed?

I'm a newbie to maths ?

 

[tkhunny]

"Average" any better? Same thing.

 

[Deleted member 4993]

Hay all, just started re-studying after 15 years, was looking for some clarity in wording/ (This is part of my question) Use these two values to calculate the average (mean) rate of change of ice coverage per year over this period.

The word mean threw me, do I find the mean of the two values, then the rate of change, or simply just take away both values and proceed?

I'm a newbie to maths ?

Can you please post the complete problem - exactly?

 

[Dr.Peterson]

Hay all, just started re-studying after 15 years, was looking for some clarity in wording/ (This is part of my question) Use these two values to calculate the average (mean) rate of change of ice coverage per year over this period.

The word mean threw me, do I find the mean of the two values, then the rate of change, or simply just take away both values and proceed?

I'm a newbie to maths ?

The mean rate of change is not the same as the mean of two values. If anything, they would probably want the slope between two points on a graph. But we really can't know what is being asked for without seeing the entire problem.

 

[Otis]

… The word mean threw me …

Hello Maths!!!!!: There are different kinds of "average" (mean, median, mode). They're instructing you to use the mean: [total change in ice area] divided by [period's total time]. (The words 'average' and 'mean' are almost always used to mean the same thing, with beginning students.)

EG:
The Wilkins Ice Shelf in Antarctica measured 14,290 square kilometers on March 1, 2008. After twenty-five days, it measured 13,860 square kilometers. Use these values to find the area's average daily rate of change.

Beginning time: 0
Beginning area: 14290
Ending time: 25
Ending area: 13860

Average rate of change = (Ending area - Beginning area) / (Ending time - Beginning time)

Average rate of change = -430/25 = -17.2

The ice shelf decreased in area an average of 17.2 square kilometers per day, during the first 25 days of March 2008.

?

 

[Steven G]

It clearly says to find the average rate of change. The average rate of change, even if you do not know what it is, is one thing. It is not the mean and the rate of change.

 

[JeffM]

Ignoring median and mode, there are three common methods to compute a mean. Each way is useful for different purposes. We cannot begin to help you understand what the best answer is unless you tell us exactly what the question is. Honestly, if you have only two values, the three methods necessarily give the same result, but if there are follow-up questions, it is likely to make a difference. It would also help us help you if we had some clue as to what you are currently studying.

 

[Maths!!!!!]

Hello Maths!!!!!: There are different kinds of "average" (mean, median, mode). They're instructing you to use the mean: [total change in ice area] divided by [period's total time]. (The words 'average' and 'mean' are almost always used to mean the same thing, with beginning students.)

EG:
The Wilkins Ice Shelf in Antarctica measured 14,290 square kilometers on March 1, 2008. After twenty-five days, it measured 13,860 square kilometers. Use these values to find the area's average daily rate of change.

Beginning time: 0
Beginning area: 14290
Ending time: 25
Ending area: 13860

Average rate of change = (Ending area - Beginning area) / (Ending time - Beginning time)

Average rate of change = -430/25 = -17.2

The ice shelf decreased in area an average of 17.2 square kilometers per day, during the first 25 days of March 2008.

?

 

[Maths!!!!!]

Thanks guys, sorry if I was a tad vague just didn't want someone to answer my question for me by mistake...

 

[JeffM]

Thanks guys, sorry if I was a tad vague just didn't want someone to answer my question for me by mistake...

We seldom give answers and never by mistake. We provide ideas if you can‘t get started, identify errors if you show us work, confirm or reject your proposed answer if you provide only that. But it greatly delays things if we do not know exactly what the problem says.

 

[Maths!!!!!]

Okay duly noted

 

[Dr.Peterson]

We seldom give answers and never by mistake.

I would say that people do give answers "by mistake", in the sense of breaking our rules. But if you explicitly state that you don't want an actual answer to the problem, that should deter most newbies who would otherwise think they were helping by doing so (or oldies who think you're demanding a full answer).

 

[Otis]

… sorry if I was a tad vague …

No worries, Maths!!!!!,

Here's some extra information, about average rate of change. Do you remember graphing lines and calculating slopes of lines? When we connect two points on a graph with a straight line, we call it a 'secant line'. Using (x,y) coordinates, the slope of that secant line is y's average rate of change, over the interval from the first x-value to the second. Here's a generalized example.



The blue curve shows increases and decreases in y-values, as x-values increase. The slope of that secant line is the average rate of change in y-values, from point A to point B.

If we had actual (x,y) coordinates for points A and B, then we could use the Slope Formula to calculate the average rate of change over the interval.

Using symbolic coordinates: (x_A, y_A) for point A and
(x_B, y_B) for point B, the Slope Formula says:

average rate of change = (y_B - y_A) / (x_B - x_A)

Note the similarity between that and the formula in my ice-shelf example. We could think of the Slope Formula as:

average rate of change = (ending y - beginning y) / (ending x - beginning x)

Picking numeric coordinates (5, 1) for A and (7, 4) for B, we get:

average rate of change = (4 - 1) / (7 - 5) = 3/2

Therefore, we could say (in going from A to B) that y's value increases an average of 3 units for a 2-unit increase in x. Or, said another way, the rate of change in y averages 3/2 units for every 1-unit change in x (over the interval from x=5 to x=7).

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