1. Statistics & Graph

Five numbers have a mean of 7. Seven numbers have a mean of 5. What is the mean of 12.

with mean you have to divide the sum of scores by the number of scores, can you help me here?

2. Originally Posted by Sazza
Five numbers have a mean of 7. Seven numbers have a mean of 5. What is the mean of 12.

with mean you have to divide the sum of scores by the number of scores, can you help me here?
You do what is called a "weighted average." The trick is that the numerator is the sum of all the scores. What is the sum of the first 5 numbers? Sum = (7)*(5 scores). Likewise for the last 7 numbers. And, of course, the denominator is the total number of scores. So:

$\text{average} = \frac{7 \cdot 5 + 5 \cdot 7}{5 + 7}$

-Dan

3. Here's the Question: An Icecream manufacturer surveyed 400 people about their favourite icecream flavours. The results are graphed in the pie graph below. The attachment is the pie graph!

i'm kinda confused hee, because when i tryed working it out (see attachment) it says i have to divide 360 by 400 and i got 90, and now supossivly from my textbook, that 90 would be the sizes of the angle at the centre. So 1 student is represented by a sector with an angle of 90 degree's but when i look at the pie graph! 908 couldn't mean 1 person becauset he pie graph has to cover 400 people, and the mere 90 degree's would be too much! Do you get me?

4. Originally Posted by Sazza
Here's the Question: An Icecream manufacturer surveyed 400 people about their favourite icecream flavours. The results are graphed in the pie graph below. The attachment is the pie graph!

i'm kinda confused hee, because when i tryed working it out (see attachment) it says i have to divide 360 by 400 and i got 90, and now supossivly from my textbook, that 90 would be the sizes of the angle at the centre. So 1 student is represented by a sector with an angle of 90 degree's but when i look at the pie graph! 908 couldn't mean 1 person becauset he pie graph has to cover 400 people, and the mere 90 degree's would be too much! Do you get me?
I'm not sure where the 90 degrees come in. (Is that possibly the size of the central angle that the "strawberry" takes up?)

To calculate how many people liked, say, chocolate:
$(400) \cdot \frac{144}{360} = 160$

You take the fraction of the central angle the wedge takes up and multiply it by 400 people. (So your 90 degree angle would represent 100 people.)

-Dan

5. so do you mean you multiply 144 (the wedge angle) by the 400? but then that would get 500 and something, and what relevance has that got with the graph? Sorry i'm just kind of torn between 2 ways i could do it! My textbook is talking about something different to how your explaining it!

6. Originally Posted by Sazza
so do you mean you multiply 144 (the wedge angle) by the 400? but then that would get 500 and something, and what relevance has that got with the graph? Sorry i'm just kind of torn between 2 ways i could do it! My textbook is talking about something different to how your explaining it!
You forgot to divide the angle by 360.

The idea here is we want the pie graph to represent the whole population of 400. So each angle is determined as the fraction of a circle represented by that same fraction of 400.

-Dan

7. Well in response kinda to my first post, it's still related to the mean etc.

The mean number of points scored per game for a netball team after 4 matches was 22. After the fifth match their average was 23. How many points were scored in their fifth match.

How would i be able to find how many scores by that?

8. Originally Posted by Sazza
Well in response kinda to my first post, it's still related to the mean etc.

The mean number of points scored per game for a netball team after 4 matches was 22. After the fifth match their average was 23. How many points were scored in their fifth match.

How would i be able to find how many scores by that?
Let $x$ be the number of points they scored in their fifth game.

then we must have: $\frac {22 \cdot 4 + x}{4 + 1} = \frac {88 + x}{5} = 23$

now the question is, why is that?

Hint: see topsquark's first post

9. Freya earns $600 a fortnight. She shares a house and has the following fortnightly budget. Essential expenses (rent, electricity, transport, phone)$345
Food and Groceries $135 Non-essential expenses (entertainment)$50
Savings $70 Draw a pie graph to show how freya’s pay is spent. Show all of the working/calculations needed. With the workings I know all how to do it, thanks to topsquark and my text book, but I just don’t see what I would need working out for? I mean all you would do is draw a pie graph and mark 345 as the bigger, than 135 as slightly smaller etc! so why do I need the calculations? Am I missing something? 10. Originally Posted by Sazza Freya earns$600 a fortnight. She shares a house and has the following fortnightly budget.

Essential expenses (rent, electricity, transport, phone) $345 Food and Groceries$135
Non-essential expenses (entertainment) $50 Savings$70

Draw a pie graph to show how freya’s pay is spent.
Show all of the working/calculations needed.

With the workings I know all how to do it, thanks to topsquark and my text book, but I just don’t see what I would need working out for? I mean all you would do is draw a pie graph and mark 345 as the bigger, than 135 as slightly smaller etc! so why do I need the calculations? Am I missing something?
in math, we like to be a bit more precise than "a little bigger than" and "a little smaller than." what does that mean? the pie chart has to be in its correct proportions, which means your calculations are to find the angles for the sectors of the pie, so that the areas of the sectors precisely match in proportion to their respective dollar amounts

11. so i would use a protractor to find an angle that would be sutible for the amount say for $50 dollars, and when we do that, the pie graph would be complete, so all the angles will have to add upto 360? 12. Originally Posted by Sazza so i would use a protractor to find an angle that would be sutible for the amount say for$50 dollars, and when we do that, the pie graph would be complete, so all the angles will have to add upto 360?
yes, find the respective proportions and then match up those proportions to the degrees of the circle.

for instance, for the $50, her total was$600, so that proportion would be: 50/600 = 1/12. so the proportion that matches \$50 would be 1/12 th of the circle, therefore, what would the central angle for that sector be?

13. it would be 30 degree's right? 12 divided by 360 = 30
anyway i'v read about a strategie in my textbook, which tells you how to find the angle at the centre of the pie graph!
Well it says any, but i inserted the info needed:
Savings Sector Angle = 70/600 of 260
= 70/600 X 360
= 41.99
angle at the centre = 41.99 but do you know whether you would narrow it up to 42?

14. Originally Posted by Sazza
it would be 30 degree's right? 12 divided by 360 = 30
anyway i'v read about a strategie in my textbook, which tells you how to find the angle at the centre of the pie graph!
Well it says any, but i inserted the info needed:
Savings Sector Angle = 70/600 of 260
= 70/600 X 360
= 41.99
angle at the centre = 41.99 but do you know whether you would narrow it up to 42?
yes, it would be 30 degrees, since that is 1/12 x 360.

yes, i'd just write 42, for the purpose of drawing the pie chart. i mean, how accurately can you measure 41.99 degrees with your protractor?

continue like that for the rest, and then draw your pie chart and you'll be done

15. Originally Posted by Jhevon
Let $x$ be the number of points they scored in their fifth game.

then we must have: $\frac {22 \cdot 4 + x}{4 + 1} = \frac {88 + x}{5} = 23$

now the question is, why is that?

well the 22 would stand for the mean score, the 4 would be the amount of games played! the 4 + 1 would be the four games then the fifth game, but i'm kinda lost as to the second lot of workings, most likely because i haven't grasped the answer from the first lot probably! how would i be able to calculate the fraction with out knowing what x equals?

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