Data, sampling and averages Problem set A

A sports club has 480 members: 200 juniors, 160 seniors and 120 veterans. A survey of 24 members is needed, with the same proportion of each group. Choosing randomly within each group.

1. (a) Name this sampling method.
2. (b) How many seniors are in the sample?

Name the sampling method in each case.

1. (a) The names of all 900 students are put into a computer, which picks 60 names at random.
2. (b) At a stadium, every 10th person through the turnstile is asked a question.
3. (c) An interviewer must ask 20 men and 20 women. She stops people in the street until both quotas are full.

The 100 m times of runners at a school sports day are recorded to the nearest second. The table shows the results.

1. (a) How many runners were there in total?
2. (b) Complete a grouped table for the classes 11.5 ≤ t < 14.5, 14.5 ≤ t < 17.5 and 17.5 ≤ t < 20.5.
3. (c) A recorded value is 16 seconds. Between which two values does the actual value lie?

Find the mean, the median and the mode of each list.

1. (a) The number of goals scored in 7 matches: 6, 9, 4, 9, 12, 7, 15.
2. (b) The ages of 10 members of a choir: 18, 22, 19, 25, 22, 31, 20, 22, 28, 24.

Find the value of x.

1. (a) The mean of 3, 7, x, 2x, 11 is 9.
2. (b) The mean of x − 2, 2x, 3x + 1, 5 is 10.

The mean time taken by 9 students to run 400 m is 82.4 seconds. A tenth student runs, and the mean of the 10 times is 84 seconds.

1. (a) Find the tenth student's time.
2. (b) A student whose time was 96 seconds is then removed from the 10. Find the mean time of the other 9 students, to 3 significant figures.

The table shows the number of books read last month by each of the students in a class.

1. (a) Find how many students there were in total.
2. (b) Find how many students had more than 3 books.
3. (c) Use your calculator to find the mean.
4. (d) Use your calculator to find the standard deviation.

A lorry waits at a depot. The table shows the waiting time, in minutes, over 20 days. The mean waiting time is 6.75 minutes.

1. (a) Write down the total frequency.
2. (b) Find the value of y.

The masses of 100 parcels in a depot are recorded in the table.

1. (a) How many parcels have a mass less than 2.0 kg?
2. (b) State the modal group.
3. (c) Estimate the mean mass.

The waiting times at a clinic, in minutes, are grouped in the table. Estimate the mean waiting time.

The mean score of 20 boys in a fitness test is 61. The mean score of all 50 students in the year is 66.4.

1. (a) Find the total score of all 50 students.
2. (b) Find the mean score of the 30 girls.

A phone company advertises: "Nine out of ten customers say our phones last for years." The claim comes from an email survey sent to 5000 customers. 120 customers replied, and 108 of them said yes.

1. (a) Find the percentage of the replies that said yes.
2. (b) Give two reasons why the advertisement may not be reliable.
3. (c) Suggest one way to get a more reliable result.

The masses, in kg, of 15 bags of potatoes are: 2.1, 2.6, 3.4, 2.9, 3.8, 2.4, 3.1, 4.2, 2.8, 3.5, 3.0, 2.2, 3.9, 3.3, 2.7.

1. (a) Use your calculator to find the exact mean.
2. (b) Complete a grouped frequency table for the classes 2.0 ≤ m < 2.5, 2.5 ≤ m < 3.0, 3.0 ≤ m < 3.5, 3.5 ≤ m < 4.0, 4.0 ≤ m < 4.5.
3. (c) Use your table to estimate the mean.
4. (d) Explain why the answers to (a) and (c) are different.

The marks of 12 students in a quiz are: 56, 61, 74, 68, 85, 61, 79, 92, 61, 70, 83, 77.

1. (a) Use your calculator to find the mean.
2. (b) Find the median.
3. (c) Find the mode.
4. (d) Find the standard deviation σx.

A town council wants to know whether residents support a new bus route. A councillor asks the first 40 people she meets at the bus station.

1. (a) Name the sampling method used.
2. (b) Give one reason why the sample may be biased.
3. (c) Suggest a better way to choose the sample.