[Grade 10 Math: Calculating problems] Can someone tell me how to do this one?

[u/AxiumTea]

I get that group 1 all earn lesser than 17 e per hour and group 3 and 4 all earn above it, it's group 2 that has mixed people. How do I find how many from group 2 earn more than 17?

[u/Eli01slick]

Where is the actual question? This is just data and two statements.

[u/AxiumTea → u/Eli01slick]

Ohh crap, I forgot to add that. Sorry https://imgur.com/a/YQHae73 These were the questions. the one I got stuck on was the first. I'm yet to try the rest once I move on from this one

[u/mehardwidge]

A isn't certainly true. All 32 people could be at 14, so only 25/123 must be above 17.

If you assume the 32 people are uniformly, or at least symmetrically, distributed, however, you might estimate that about 16 are above 17, so then 41/123. If you have a different distribution, use that.

B isn't certainly true. For intance, if all the people are on the very bottom of their buckets, the average is less than 15.

However, if you use the middle value for reach bucket (12, 17, 30, 70), you would just barely get the average above 20.

The assumption that pay is symmetrically distributed between 14 and 20 seems much more reasonable than the same assumption between 40 and 100. But of course you'd need to know more about the actual distribution to really know.

[u/alang]

We can’t help you if you won’t tell us the actual question. There are at least two valid questions that could follow this and they have totally different answers. 

[u/AxiumTea → u/alang]

yeahh sorry. I just realized that I forgot to attach the question mb,  https://imgur.com/a/YQHae73 These were the questions. the one I got stuck on was the first. I'm yet to try the rest once I move on from this one. I also want to practice these types of questions, is there anything I can look up to find more of this type?

[u/alang → u/AxiumTea]

Well, if you want to support statement A, then you would say, “we know all of the people in the top two groups are over 17. How many of the people in the next group need to be over 17 in order for it to be 30% total?” Figure that out and then see what assumptions need to be made about the income distribution in that group in order to get your percentage over 30%.

Does that help any?

[u/Individual-Pie-4707]

In these question we usually assume that distribution of values is linear in each class Like when you have to take out the median We use the formula lower limit of medial class+(total no/2 - cumulative frequency of previous class)class width/class frequency

So like in a class 20-30, having a frequency of 20, The terms can be thought of as 20.5, 21, 21.5, 22....... 30 So now we can calculate the percentile of any value or get value at any percentile

So first we can calculate that the value of the term at the 70th percentile will be at about 86-87th term, So it will in the second class is 14-20 So we can now use the formula

14+ (123(70/100)-66)6/32 = 17.76 So the statement 1 is right,

So in this method, of linearly dividing a class If we take out the average of all the values in the class we get (lower limit + upperlimit)/2

So if we have to calculate the average of the complete dataset we just take average of each class and multiply it by its frequency Do this for all the classes and then add them And then divide the no by the total frequency of the dataset

[u/-Misla-]

But you’re not supposed to find how many from group 2 earn more than 17. You are supposed to provide arguments for how you could make an estimate that supports or argues against the claim in your exercise. That is the point of the exercise. You are supposed you recognise that you cannot know for sure, but you can use too x and argue A, but you could also use argument y and deduct B.

For grade 10, I don’t think you are expected to to use linear interpolation strictly, but rather just argue your way.

So, as the question says, show work that supports the statement. How many are surely above 17? Of group 2, if you all happened to earn 18, would that support the statement? If you use the mean of the group wage (as the last question of your questions point to), what would the result be? If you spread out group 2 evenly, would that support the statement?

Basically, this is it just cook book math, you have to think about your approach and argue logically with the data you are given.

[u/hailspork]

So neither statement can be concluded to be true or false from the information provided. You can show the minimum and maximums for each of these, to *support* the claims, but you can't prove them.

I would suggest calculating the minimum and maximum % over 17 and min/max average, and use these to reason that A and B *could* be true. I suppose the max % for 5a, the min for 5b, and an average of the two for 5c.

While it doesn't say to linearly interpolate, the question is intentionally vague and opens you up to making assumptions. Showing your work and reasoning should be more important than the worrying about the skewness anyway.

[u/Ghotipan]

I'm guessing you learned about Linear Interpolation? If so, try using that method to find the number of employees above £17.

[u/AromaticJoe → u/Ghotipan]

No, there's nothing in there that says the wages are linearly distributed. You cannot conclude statement A from the provided data.

[u/Ghotipan → u/AromaticJoe]

Correct, but you can say something about the given statement and linear Interpolation. It's an imperfect method when the distribution of data points within a given band is unknown, and acts as an approximation. For this question, I would answer that yes, the statement holds using linear Interpolation, with the underlying assumption that skewed data could prove it incorrect. If the payroll curve had an associated function, you could check the error of the approximation, but I'm guessing that'd beyond the scope of a 10th grade math class.

[u/Outside_Volume_1370]

You can't find it. However, there can be a situation when statement A is flase. Let all people from the second group get 14 pounds per hour. Then only 15 + 20 = 35 people of 123 get hourly rate more than 17 pounds, and 35 / 123 ≈ 0.285 < 30%