Measures of location

A maths teacher holds a revision session every Wednesday.

In a random sample of eight Wednesdays, the number of students who attended is listed below.

2 4 3 1 4 5 2 3

Find the mean of these eight values.

Find the variance of these eight values.

The teacher believes that the number of students who attended a revision session each Wednesday can be modelled by the binomial distribution B(30, 0.1).

Comment on whether the mean and variance found in parts (a) and (b) support the teacher’s belief.

Fully justify your answer.

The teacher wanted to decide if a Saturday morning revision session was worth doing.

The teacher asked the first 10 students who entered the classroom if they would attend a Saturday session.

Name this method of sampling.

Describe one advantage of this method of sampling.

In a particular year, the height of a male athlete at the Summer Olympics has a mean 1.78 metres and standard deviation 0.23 metres.

The heights of 95% of male athletes are between 1.33 metres and 2.22 metres.

Comment on whether a normal distribution may be suitable to model the height of a male athlete at the Summer Olympics in this particular year.

You may assume that the height of a male athlete at the Summer Olympics may be modelled by a normal distribution with mean 1.78 metres and standard deviation 0.23 metres.

Find the probability that the height of a randomly selected male athlete is 1.82 metres.

Find the probability that the height of a randomly selected male athlete is between 1.70 metres and 1.90 metres.

Two male athletes are chosen at random.

Calculate the probability that both of their heights are between 1.70 metres and 1.90 metres.

The summarised data for the heights, h metres, of a random sample of 40 male athletes at the Winter Olympics is given below.

Use this data to calculate estimates of the mean and standard deviation of the heights of male athletes at the Winter Olympics.

Using your answers from part (c), compare the heights of male athletes at the Summer Olympics and male athletes at the Winter Olympics.

The table below is an extract from the Large Data Set.

Calculate the mean and standard deviation of CO₂ emissions in the table.

Any value more than 2 standard deviations from the mean can be identified as an outlier.

Determine, using this definition of an outlier, if there are any outliers in this sample of

Fully justify your answer.

Maria claims that the last line in the table must contain two errors.

Use your knowledge of the Large Data Set to comment on Maria’s claim.

Using the box plot, give one comparison of central tendency and one comparison of spread for the two regions.

Comparison of central tendency

Comparison of spread

Jaspal, an environmental researcher, used all of the data in the Large Data Set to produce a statistical comparison of the CO₂ and CO emissions in regions of England.

Using your knowledge of the Large Data Set, give two reasons why his conclusions may be invalid.

Amelia decides to analyse the heights of members of her school rowing club.

The heights of a random sample of 10 rowers are shown in the table below.

Any value more than 2 standard deviations from the mean may be regarded as an outlier.

Verify that Ann’s height is an outlier.

Fully justify your answer.

Amelia thinks she may have written down Ann’s height incorrectly.

If Ann’s height were discarded, state with a reason what, if any, difference this would make to the mean and standard deviation.

A survey of 120 adults found that the volume, X litres per person, of carbonated drinks they consumed in a week had the following results:

Calculate the mean of X.

Calculate the standard deviation of X.

Assuming that X can be modelled by a normal distribution find

P(0.5 X 1.5)

P(X 1)

Determine with a reason, whether a normal distribution is suitable to model this data.

It is known that the volume, Y litres per person, of energy drinks consumed in a week may be modelled by a normal distribution with standard deviation 0.21

Given that P(Y 075) 010, find the value of , correct to three significant figures.