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My answer to problem (3):
It is said that Oliver is 10% taller than Jack.
Jack is 170cm tall.
How much taller is Oliver than Jack ?
10% is equivalent to 10 parts of 100 equally divided parts.
It is therefore the same as dividing by 10.
So you could do 170 / 10 = 17
Or with a calculator you could do 0.1 x 170 = 17
17cm
How tall is Oliver ?
Obviously just add on the 17 to 170 being careful about place value.
170 + 17 = 187
187cm
That is a good point. I had assumed that the sample figures were intended as the weights - in that they represented the 'units' of concern for the
purposes of the average. It does look like you don't have any data to 'weigh' the hotel so to speak. It depends on the context of what you are trying
to do. For instance if this is a very big hotel chain, then you might look at the turnover figures for the hotels, or the number of customers per year,
in general something that gives an idea of the scale of importance in relative terms for different hotels.
Why were the sample sizes different I wonder? I was assuming that the sample size varied in proportion to how 'big' the hotel was.
Perhaps it just depends upon how much data you have for each hotel and not necessarily the prominence of the hotel per se.
It looks like it is not strictly possible to obtain a weighted average with the information you have given, but it is common practice in statistics to
work out a weighted average by the multiplication that I described:
weighted average = sum of ((score of item) x (frequency of item)) / sum of (frequency of item)
Imagine that you had not summarised them in a table, but had all of the individual scores in a list then the above formula would give the same averages.
If the sample size is not the population size, and is not proportional to it, then it is not strictly speaking a frequency suitable for weighted averages.
On the other hand the scores were presumably worked out by dividing the total row score by each sample size for each row so it is
reasonable to get an overal average by reversing this division.
I think you have to take each pair of Score and Sample size and multiply them, and then add these together to get a total,
then divide by the total sample size for all of the rows you have added:
eg. (3.83 x 521) + ..... + ...... I have just given the first row of the scores x sample sizes (I won't add all of them because there are a lot - and also that is your job)....
Then add 521 + 806 + ..... and get the sample size total
Remember to treat each year separately of course for both totals in each case.
(Similar principle for the top table except that they are not years, and similar I think for the percentages,
just treat them like scores - multiply them by the sample sizes in each row - then sum them - then divide by the total sample size.
I notice that the total sample sizes are there already and that the averages are already given.)
My answer to problem (2)
Am amount of £160 plus VAT is quoted by a supplier.
The VAT rate is 20%
How much is the 20% VAT ?
If you are doing this in your head or on pen and paper you could convert
20% into a fraction by regarding it as 20 parts of 100 equally divided
amounts which cancels to one part of five equally divided amounts.
You could then work out 160 divided by 5 which is 32.
When using a calculator I would just write:
0.2 x 160 = 32.00
£32.00
How much is the amount after adding VAT ?
This is just an addition of 160 + 32 = 192
£192.00
My answer to problem (1):
£490 is put in a savings account for a year with a rate of 3%
No money is taken out and no more is put in during the year,
and the amount of interest paid is exactly 3%
How much does the person receive in interest ?
The percentage 3% should be regarded as three of one hundred equally divided
parts of the amount. So we could divide £490 by 100 to give us £4.90 and then
multiply by 3 to give us £14.70. If you are using a calculator this is a rather
slow way round things, but at GCSE level you would be expected to understand
both methods:
So either 3 x 490 / 100 = 14.70
or with a calculator you can do this: 0.03 x 490 = 14.70
£14.70
What is the total amount after this is added to £490 ?
This is just a simple addition. Care must be taken to line up the
decimal point if you are using pen and paper for this, but using
a calculator you just have to be careful with typing the right keys:
14.70 + 490.00 = 504.70
£504.70
Wouldn't it be more conventional to give the answer as:
I agree it is an upwards round and that you should keep the zero.
Here are a few problems that I have made up for you to look at and attempt when you are ready:
Problem (1)
£490 is put in a savings account for a year with a rate of 3%
No money is taken out and no more is put in during the year,
and the amount of interest paid is exactly 3%
How much does the person receive in interest ?
What is the total amount after this is added to £490 ?
Problem (2)
Am amount of £160 plus VAT is quoted by a supplier.
The VAT rate is 20%
How much is the 20% VAT ?
How much is the amount after adding VAT ?
Problem (3)
It is said that Oliver is 10% taller than Jack.
Jack is 170cm tall.
How much taller is Oliver than Jack ?
How tall is Oliver ?
You may of course use your calculator for these.
To be perfectly honest I don't know how your other computer works because I have not had one of that type before.
Perhaps Bob has an idea. I have sent you an email just a moment ago.
Do have a good look at the last few posts including my answers.
Try to understand how I have got my answers and follow each and every calculation with the help with your calculator.
I will be online for a meeting with you on Monday at 7pm.
If you do on your calculator: 70 divided by 560 = ....
then you get 0.125
Let us assume the calculator is correct. This is the decimal equivalent of (70 / 560).
If you then do multiply by 100 to this number you get: 12.5
This is the figure for the percentage (12.5%).
You can use your calculator for these.
Okay I was thinking about this fraction: (70 / 560)
What is that as a decimal ?
What is it as a percentage ?
Right Andrew had £70 out of £560. So how do you calculate the decimal of the proportion that he is given ?
Here are the answers to those exercises from two days ago:
Problem (1)
What is 20% of £500 ?
£500 x 0.2 = £100
What is 25% of £700 ?
£700 x 0.25 = £175
Problem (2)
Of £560 shared out, Andrew is given £70, Luke is given £105, Karen is given £245,
Chloe is given £140. What percentages have each been given?
Answer:
Andrew is paid 12.5%
Luke is paid 18.75 %
Karen is paid 43.75 %
Chloe is paid 25 %
Problem (3)
Of £810 shared out, £360 is given to Peter, £405 is given to Thomas and £45 is given to Carl.
What percentages of £810 are these to one decimal place accuracy ?
Answer:
Peter is paid 44.4 %
Thomas is paid 50 %
Carl is paid 5.6 %
Q1: Round to the nearest whole number 4.7 ?
Answer: 5
Q2: Round to the nearest whole number 7.5 ?
Answer: 8
Q3: Round to the nearest whole number 3.2 ?
Answer: 3
Bye.
Let us make it 7pm on Saturday.
Here is a recap on some rounding problems that I have posted two months ago:
Q1: Round to the nearest whole number 4.7 ?
Q2: Round to the nearest whole number 7.5 ?
Q3: Round to the nearest whole number 3.2 ?
I have got a few percentage problems which are these:
Problem (1)
What is 20% of £500 ?
What is 25% of £700 ?
Problem (2)
Of £560 shared out, Andrew is given £70, Luke is given £105, Karen is given £245,
Chloe is given £140. What percentages have each been given?
Problem (3)
Of £810 shared out, £360 is given to Peter, £405 is given to Thomas and £45 is given to Carl.
What percentages of £810 are these to one decimal place accuracy ?
Anything between 0.5 and 1.0 would round to 1
Anything less than 0.5, but higher than 0 rounds to zero.
So 0.49 rounds to zero.
(Obviously this is when rounding to the nearest whole number, I will have to go into
rounding to a certain number of decimal places separately.)
If the number has a five after the decimal place then conventionally we usually round upwards.
So 0.5 rounds to 1 even though it is as near to one as to zero.
and 1.5 rounds to 2 even though it is as near to two as to one.
I was expecting 3% as an answer to that one.
Yes good.
Right now the second part of my question asks you to round off the percentages to the
nearest whole number and then work the two out which would change (2.5% and 18.5%)
to see by how much the answer changes as a result of this.
So: What is 2.5 % rounded to the nearest whole number using a conventional rounding method ?
Good right so can you gather those answers together to answer the first part of the question:
Abigail is paid 75% of £600
Emma is paid 4% of £600
Michael is paid 2.5% of £600
Daniel is paid 18.5% of £600
How much money in pounds is each person paid ?
What is 18.5% of £600 ?
With the 2.5 % of 600 you did:
2.5 x 600 = 1500
It was supposed to be:
0.025 x 600 = 15