Data, sampling and averages Problem set B

A hospital has 360 staff: 150 nurses, 120 doctors and 90 administrators. A survey of 36 staff is needed, with the same proportion of each group. Choosing randomly within each group.

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

Name the sampling method in each case.

1. (a) All 350 raffle tickets are numbered and a random number generator picks 25 of them.
2. (b) At a car park, every 8th car that arrives is asked about the parking charge.
3. (c) A market researcher must interview 15 people under 30 and 15 people aged 30 or over. She asks whoever passes until both quotas are full.

The lengths of long jumps by pupils on a sports day are recorded to the nearest centimetre. The table shows the results.

1. (a) How many pupils were there in total?
2. (b) Complete a grouped table for the classes 449.5 ≤ l < 452.5, 452.5 ≤ l < 455.5 and 455.5 ≤ l < 458.5.
3. (c) A recorded value is 455 centimetres. 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 emails received on 7 days: 21, 14, 17, 14, 9, 25, 14.
2. (b) The shoe sizes of 10 students: 3, 8, 5, 6, 8, 11, 4, 8, 7, 10.

Find the value of x.

1. (a) The mean of 5, 8, x, 3x, 14 is 11.
2. (b) The mean of x + 1, 2x − 3, 3x + 2, 8 is 11.

The mean mass of 11 eggs is 58.5 g. A twelfth egg is added, and the mean mass of the 12 eggs is 59.2 g.

1. (a) Find the mass of the twelfth egg.
2. (b) An egg of mass 52 g is then removed from the 12. Find the mean mass of the other 11 eggs, to 3 significant figures.

The table shows the number of goals scored by a hockey team in each of its matches this season.

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

A fruit farmer weighs the fruit picked from 20 trees. The table shows the mass of fruit per tree, in kg. The mean mass is 8.55 kg.

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

The heights of 80 seedlings in a nursery are recorded in the table.

1. (a) How many seedlings have a height less than 16.5 cm?
2. (b) State the modal group.
3. (c) Estimate the mean height.

The lengths of phone calls to a shop, in minutes, are grouped in the table. Estimate the mean length of a call.

The mean time of 12 sprinters from one athletics club is 11.8 seconds for 100 m. The mean time of all 30 sprinters at a meeting is 11.5 seconds.

1. (a) Find the total of the times of all 30 sprinters.
2. (b) Find the mean time of the other 18 sprinters.

A shampoo maker advertises: "Eight out of ten users prefer our shampoo." The claim comes from a form on the company's website, sent to 6000 users. 150 users filled it in, and 120 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 times, in seconds, taken by 15 pupils to solve a puzzle are: 12.4, 18.1, 15.6, 22.3, 13.8, 17.2, 26.0, 14.9, 19.5, 16.3, 21.7, 12.9, 24.1, 18.8, 15.2.

1. (a) Use your calculator to find the exact mean.
2. (b) Complete a grouped frequency table for the classes 10 ≤ t < 15, 15 ≤ t < 20, 20 ≤ t < 25, 25 ≤ t < 30.
3. (c) Use your table to estimate the mean.
4. (d) Explain why the answers to (a) and (c) are different.

The scores of 12 players in a game are: 48, 55, 62, 71, 55, 83, 67, 55, 90, 74, 59, 66.

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 gym owner wants to know whether members would like longer opening hours. She asks the first 50 members who arrive on Monday morning.

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.