Students Sheet Percentage Use and Abuse

Students’ sheet –Percentage Use and Abuse

1. A medical study to investigate whether aspirin could reduce the number of heart attacks was carried out over 5 years at Harvard Medical School. Each of the 22 071 male physicians was randomly assigned to one of two groups. One group took aspirin whilst the others took a placebo, a tablet which is thought to have no effect on the patient at all.

In the aspirin group, 104 out of 11037 subjects had a heart attack during the 5 year period. In the placebo group, 189 out of 11034 had a heart attack during the 5 year period.

A headline claims

(i) Is this claim accurate?

(ii) Re-write the headline using the changein absolute risk.

(iii) What information do you feel the report should contain to enable the reader to accurately assess the benefits of taking aspirin, and any risks involved?

2. A company has seen its profits rise and as a result it decides to increase the hourly wages of its employees.

There are two suggestions:

• To give every worker a £0.50 per hour pay rise.
• To give every worker a 1% pay rise.

Examine these suggestions from the perspective of the company and as an employee, commenting on the advantages and disadvantages of each suggestion.

3. One newspaper headline claims

Further into the story the reporter writes that Apple spends a paltry 2% of revenues compared with 14% at Google and Microsoft.

Can you conclude from these figures that Apple does spend far less on R&D?

4. A poster on the London tube advertised property in Corby (a town about an hour and twenty minutes from London).

The headline was 259% cheaper than in London.

There are several complaints about the poster.

In response the poster company explains that the figure uses information from the BBC house price guide

The company responsible for the poster states that the average house price in Corby is £126 569 whilst in Greater Landon the average house price is £454 644.

This makes the average price difference £454 644 – £126 569 =£328 075

So the percentage increase from Corby to Greater London (328075 ÷ 126 569) x 100 = 259.2… which makes the 259% quoted in the poster.

Is it really cheaper 259% to live in Corby than London?

5. During the US presidential election, some newspapers covered a story about the amount of tax apportionedto benefits changing from6.2 % to 4.2 %of the average American's taxable income.

This was described as a 2%cut.

Does this seem like a large or a small change?

6. A shop owner raises the price of a pair of £100 shoes by 50%.

After a few weeks because of falling sales the owner reduces the price of the shoes by 50%.

Are the shoes back to the original price?

7. The annual number of burglaries in a town fell by 40% in 2012 and then by 30% in 2013.

Does this mean the number of burglaries has fallen by 70% over the two year period?

8. To prevent the spread of measles and other viruses, people are encouraged to be vaccinated.

This is because people who have been vaccinated generally don’t get the virus and, consequently, the number of healthy people in the population at risk of contracting the virus is reduced.

The number of people with a virus will increase only if each person with the virus gives the disease to more than one healthy person. This assumes that those who have the virus do eventually get better.

On average, during the course of their illness, someone with measles will expose 20 people to the infection. What percentage of the population would have to be vaccinated to prevent the spread of measles?

9. A manager wants to compare the effectiveness of two female employees; Angela and Bertha.She monitors their performance on two days. She asks customers if they are satisfied with the service they received and the results are shown below. As the employees work different hours on each of the two days she chooses to use the percentage of satisfied customers on each day to compare their performance. The manager tries to give the employees a random selection of customers to avoid any bias in the sample.

After viewing these results the manager decides Angela is the better employeeand tells Bertha she should learn fromAngela.

Bertha complains, and the manager examines the data in more detail.

Who seems to be the better employee?

10. In 1973 the University of California at Berkeley was accused of gender bias in its admissions. When the total admissions from 6 departments were examined the results appeared to the protestors to show gender bias.

The college denied the claims and quoted the figures for its individual departments.

Was the college’s admission policy biased?

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