What percentage of passengers survived the Titanic disaster?

Here is a link to download an Excel spreadsheet. This spreadsheet contains the names of more than 1,000 people who were travelling on the Titanic when it went down. For each person it also lists their age, gender, the class of their ticket (1st, 2nd, and 3rd), and whether or not they survived.

First you are going to calculate the overall percentage of people who survived. Instructions on how to calculate this in Excel are given here. Write down the number you get.

Now I want you to pretend that you don’t have all this data sitting in front of you. All you have is the list of passengers. You want to find out what percentage of the passengers survived, but you don’t have the time to dig up that information for every single one. You therefore decide to estimate the number by just looking at information for 100 people.

Randomly select 100 passengers from the list (again, instructions on how to do this easily in Excel are given here). What percentage of this sample survived? How similar is this number to the actual percentage of the whole list who survived? In other words, how close was your sample-based estimate to the truth? Remember, in real life we don’t know what the ‘real’ answer is – we only have the estimate from our sample.

You can try this a few times, selecting a different random sample each time. What kind of estimates do you get back? How often do you get a ‘weird’ sample where almost everyone survived, or almost everyone died?

Something you will have seen if you ever watched the news on TV (or listened to it on the radio) is the ‘vox pop’. This is where the presenters stand around in a city centre or shopping mall, accosting passers-by for their opinions on today’s big news event (an election debate, a flood, a high-profile criminal case). The intention of these vox pops is the same as that of a sample survey – to try to get an idea of the public’s opinion on a particular topic.

Think of something you could do a vox pop about. Don’t worry, I’m not going to ask you to actually talk to people. Just think about your local town centre. If you were to interview some of the people there, what type of people do you think you would end up speaking to? How would these people differ from the population at large? How do you think this would affect your estimate of what the public think about the issue you’ve chosen?

In December 2015, the British Independent newspaper published a story headlined “Brighton is the most attractive city in the UK (according to Brighton)”. This story was based on a survey conducted by the polling company YouGov. YouGov asked the residents of 15 British cities how they would rate the attractiveness of their fellow townsfolk.

The table below gives the percentage of people in each city who rated people where they lived as very or fairly attractive:

The overall sample size for this survey was 1,500 people; 100 people in each city. We’ll assume that the sampling procedure was appropriate (i.e. a random probability sample within each city).

Using your knowledge of the estimates and the sample size in each city, explain the problem with using the results of this survey to derive a ‘league table’ of attractiveness.