Sunday, 30 October 2016

Quibans 46: Commuting in London

From the London Evening Standard:

One in three Londoners lose one day every week from commuting
A third of Londoners spend the equivalent of a whole day’s work every week commuting to and from the office, a study revealed today.
The findings were revealed in the annual London Commuter Index which looks at attitudes towards daily commutes.
It found that 30 per cent of workers spent an average of eight hours and 45 minutes a week on their commute, and 31 per cent were commuting for an average of six hours and 15 minutes.
Cost of travel was also shown to put workers under financial strain, with more than half spending an average of £1,500 on annual season tickets — the equivalent of paying the average London rent for about two months.
Three quarters of Londoners said reducing this expense would improve their journeys.
To beat rush-hour blues more than 64 per cent of commuters said they listened to music — and more than one in 10 practised mindfulness during their journeys.
About 61 per cent of people thought overcrowding was the worst part of commuting, while 28 per cent said it was delays. A survey of Tube passengers found a third liked the Victoria line best, while 36 per cent said the Central line was worst and would be improved by air conditioning.
The survey was carried out by season ticket loan company CommuterClub which quizzed 554 customers.


Questions:

1)  How many people made each statement? 

2)  How long is each journey if the total in the week is 8 hours 45 mins?

3)  If everyone not mentioned has an average commute of 3 hours, what is the average commute for everyone in London?

4)  Which part of the article doesn’t seem sensible? 

5)  How might they have collected the data?
What can we do with the information about the cost of the tickets?

Answers:

1)  How many people made each statement? 
% given
lower bound
'exact'
upper bound
lowest integer
highest integer
30%
163.43
166.2
168.97
164
168
31%
168.97
171.74
174.51
169
174
75%
412.73
415.5
418.27
413
418
64%
351.79
354.56
357.33
352
357
10%
52.63
55.4
58.17
53
58
61%
335.17
337.94
340.71
336
340
28%
152.35
155.12
157.89
153
157
33.333%
181.8967
184.6667
187.4367
182
187
36%
196.67
199.44
202.21
197
202
[To work out the final two columns I used the Excel formula “Ceiling.Math” and “Floor.Math”]

2)  How long is each journey if the total in the week is 8 hours 45 mins:  This is 525 minutes.  Divide it by 10 (5 days of travelling there and back) to get 52 and a half mins per journey.

3)  Average:  5 hours 44 mins

4)  Which part of the article doesn’t seem sensible:   How will having a cheaper ticket make the journey more bearable?  Do people get grumpy at delays and overcrowding and then get even crosser because they are paying lots for the privilege?  Or would they be able to afford more takeaway coffee if the tickets were cheaper?

5)  How might they have collected the data:  Asking people at different stations.  Emailing those who use their website.  Are there any problems with this?




Quibans 45: Army fitness

From the Daily Telegraph:
Army fitness slips, but female soldiers close the gap on menThe proportion of Army soldiers failing fitness tests has nearly doubled in three years amid concerns that personnel are losing focus because they are not being sent to war.
Female troops are also narrowing the gap with their male counterparts after years of falling behind, The Telegraph can disclose.
In 2013, 7,120 - or 9.6 per cent - of the ### personnel who were made to complete personal fitness assessments failed at least one, according to figures released by the Ministry of Defence (MoD).
In comparison, between January and mid-September this year ### troops - around 17.7 per cent - out of a possible 63,910 tested failed one or more.
Three years ago, just over 12 per cent of females tested failed at least once, while 9.4 per cent of men did. This year, 18.8 per cent of women and 17.6 per cent of men failed one or more assessments.  
One recently retired Army officer suggested that soldiers were finding it more difficult to focus on keeping fit because they knew they were not going on operations.
He said: "Operations sharpen the mind and focus your efforts on keeping fit - the prospect of going to Afghanistan was certainly an incentive to get fit. After all you don't want to let your mates down by being unfit and not prepared. Being shot at is hard enough when you're fit, let alone when you're out of shape."

Questions:
1)  There are some blanked out numbers to calculate.
2)  In what way are the female soldiers “closing the gap”?
3)  From these figures there clearly aren’t the same number of men and women who were tested.  What is the ratio of men to women?

Comment:
If you have used any of the others that focus on rounded values, you could ask students at this stage what the upper and lower bound is for each blanked out number.

Answers:
1)  Here is the unedited excerpt:
In 2013, 7,120 - or 9.6 per cent - of the 74,010 personnel who were made to complete personal fitness assessments failed at least one, according to figures released by the Ministry of Defence (MoD).
In comparison, between January and mid-September this year 11,300 troops - around 17.7 per cent - out of a possible 63,910 tested failed one or more.
Here are the upper and lower bounds for each calculation (note that the numbers of troops might be rounded to the nearest 10 or might be exact – we can’t tell).
7120
9.6
74167
7120
9.55
74555
7120
9.65
73782
17.7
63910
11312
17.65
63910
11280
17.75
63910
11344

2)  The gap between the performance of the men and the performance of the women is smaller.  Given that both have got worse that doesn’t seem like a result to be excited about!

3)  This is interesting.  I haven’t thought about this sort of thing before.  In 2013, 9.4% of the men and 12% of the women are 9.6% of the total.

If the number of men is m and the number of women is w then we have

9.4m + 12w = 9.6(m+w)
2.4w = 0.2m
12w = m
So there are 12 times as many men as women.

In 2016, 17.6% of the men and 18.8% of the women are 17.7% of the total.
17.6m + 18.8w = 17.7(m+w)
1.1w = 0.1m
11w = m
There are 11 times as many women as men. 

This might mean that there are now more women in the army than there used to be, or that more women were tested second time around, or that the percentages given were not exact …


Quibans 44: Glastonbury

Glastonbury 2017 tickets sell out in less than an hour as music fans complain about festival website crashing
Bad news for anyone still hoping to make it to Glastonbury Festival 2017: over 100,000 tickets sold out this morning before 10am, amid complaints that the ticketing website was crashing
The coveted tickets were released this morning at 9am and were all gone before 10.  The festival organisers posted the tweet below, breaking the news to disappointed music fans, at 9.54am.

A smaller batch of  15,000 tickets with coach packages, released on Thursday last week, are also all gone, selling out within 23 minutes.

Questions:
  1. What is the rate at which the tickets sold?
  2. What is the rate at which the ‘tickets with coach packages’ sold?
  3. What is the combined rate for both types of ticket?
  4. How long did each standard ticket take to sell?
  5. How long did each ‘ticket with coach package’ take to sell?
  6. How long did each ticket take to sell on average?


Comments:
It is necessary to choose units here.  This could be ‘number of tickets per minute’ (or per second, or per hour).  The other big idea is that when combining both types of ticket we can’t just take the average.  We need to use the total number of tickets divided by the total time.



Quibans 43: Buy Apple in the Big Apple

A news website called Fast Company has this:

Due to Apple price hikes in the U.K., it’s now cheaper for Brits to fly round-trip to the U.S. to buy a MacBook Pro
On Thursday, Apple raised prices by as much as £500 on its products sold in the U.K.—thus making it cheaper to buy a round-trip ticket to the U.S. or Canada to buy your latest device and fly back to London, reports the Financial Times. For example, a MacBook Pro just jumped in price from £2,499 to £2,999,



Question:
1)  Is it true?   Here’s an opportunity to do some research and to find out.
2)  Are there any other products for which this is true too?
You might want to display the headline only and to ask for comments about that.  This appears to come from a Financial Times article, but that is paywalled. 


Comments:
2)  Various other things have risen in price (reportedly) recently, from Marmite to tea bags.  Presumably it doesn’t make sense to fly to the USA to save 20p on a jar of Marmite.  It also doesn’t seem sensible to buy a fridge in the US because the cost of shipping it to the UK would more than wipe out any saving.  A car would also have shipping costs, but worse than that it would be incompatible with the UK, because the steering wheel would be on the ‘wrong’ side (while legal to drive it would be annoying).  Which other goods fall into these categories?
Small electronic devices (like laptops and iPads) would seem to be ones it would be sensible to fly to the US to buy.  Are these the only things?



Saturday, 29 October 2016

Quibans 42: Brexit 1

A Daily Telegraph article about Brexit featured this graphic:




We did lots of things with this.

Questions:
1) Which country is each of the ‘financial capitals’ in?
2) We know the number of financial employees and the % of total employment that is financial services, so how many workers are there altogether?
3) What is the percentage increase/decrease in rent if you move from London to each of the other cities?
4) Comment on the diagrams that are used.
5) In which country is beer overpriced?

Comments/Answers:
1) We talked discussed the reasons why Berlin isn’t the financial centre of Germany.
2) We divided the first column by the percentage column and expected that this would give the population of the city. The numbers seemed to be far too big. We then decided that the percentage column (financial services as a percentage of total employment) is actually a percentage of the whole country and not the city.
3) This was straightforward.
4) Comment on the diagrams:
a. Number of financial employees: seems to use area – this is appropriate.
b. Financial services as a %: the whole bar is 18.6% – the rest are compared to this.
c. The beer seemed particularly odd. The cost of one pint of beer is shown with several full and partially filled pint glasses, where each full glass stands for £1. It seems rather odd to have 3½ pint glasses standing for the £3.46 price of one pint.
d. We didn’t like the taxi graphic much either.
5) To find out where beer is overpriced we compared the price of a pint to the taxi journey in each country and also to the average rent.

Source: http://www.telegraph.co.uk/business/2016/10/11/the-city-exodus-is-already-happening-it-just-doesnt-look-like-yo/




Friday, 28 October 2016

Quibans 41: Phil Collins

From the Daily Telegraph:

Phil Collins and the rise of mid-lifers drinking their way to oblivion
For Phil Collins it started at home in the long afternoons, drinking a glass of two or wine in front of the England versus West Indies Test match.  In 2011 the former Genesis frontman had decided to retire from music and move to Switzerland to devote himself to his family."I stopped work because I wanted to be a dad at home,” he said in a press conference on Monday in which he announced a comeback tour. “As bad luck would have it, as soon as I retired, my family split up. I didn't have anyone to go home to. That's why I started drinking."


Questions:
1)  How much is one unit of neat alcohol?
2)  How many units will 1 litre of each drink contain?
3)  If someone drinks 15 units in a week then it ought to be spread over 3 days.  That suggests 5 units as a maximum in one session.  How many of each drink is that?
[To be clear: drinking lots wasn't a good thing for Phil Collins.  Don't try this at home.]

Here is the table again, suitable for copying and pasting into a spreadsheet:
Drink
ABV*
Size
Alcohol
ABV
Size in ml
Units of alcohol
Wine
14%
125ml glass
1.8 units
14%
125
1.8
Wine
14%
175ml glass
2.5 units
14%
175
2.5
Wine
14%
250ml glass
3.5 units
14%
250
3.5
Wine
14%
750ml bottle
10.5 units
14%
750
10.5
Beer
2.80%
Pint
1.6 units
2.8%
568
1.6
Strong beer
4.80%
Pint
2.7 units
4.8%
568
2.7
Vodka
40%
25ml shot
1 unit
40%
25
1
Vodka
40%
50ml double
2 units
40%
50
2
Flavoured cider
4%
330ml bottle
1.3 units
4%
330
1.3


Answers:
It appears from the spreadsheet that 10ml of alcohol is 1 unit.  Note the rounding errors. 
Note also how the rounding errors affect the number of units that are in 1 litre of wine, as calculated from the different glass/bottle sizes.

Drink
ABV*
Size
Alcohol
ABV
Size in ml
Units of alcohol
Amount of alcohol
Drinks for 5 units
Units in 1 litre
Wine
14%
125ml glass
1.8 units
14%
125
1.8
17.5
2.8
14.4
Wine
14%
175ml glass
2.5 units
14%
175
2.5
24.5
2
14.3
Wine
14%
250ml glass
3.5 units
14%
250
3.5
35
1.4
14
Wine
14%
750ml bottle
10.5 units
14%
750
10.5
105
0.5
14
Beer
2.80%
Pint
1.6 units
2.8%
568
1.6
15.904
3.1
2.8
Strong beer
4.80%
Pint
2.7 units
4.8%
568
2.7
27.264
1.9
4.8
Vodka
40%
25ml shot
1 unit
40%
25
1
10
5
40
Vodka
40%
50ml double
2 units
40%
50
2
20
2.5
40
Flavoured cider
4%
330ml bottle
1.3 units
4%
330
1.3
13.2
3.8
3.9

Quibans 68: Human Chain

 from the Daily Telegraph: Beachgoers form incredible human chain to save drowning family   T his is the incredible moment st...