Note: Use Q1, Q2, Q3 from GCSE.
Q4
The table below shows the average amount spent per week per household on alcohol in the United Kingdom for the months March to August in 2019 and 2020.
By finding the mean and range for each year, how does the amount spent on alcohol compare from 2020 to 2019?
Answer: The mean amount spent on alcohol in 2020 was higher and the range was also greater compared to 2019.
Wrong Answers:
The mean amount spent on alcohol in 2020 was higher, but the range was smaller compared to 2019.
The mean amount spent on alcohol in 2020 was lower and the range was also smaller compared to 2019.
The mean amount spent on alcohol in 2020 was lower, but the range was greater compared to 2019.
WORKING:
Mean for 2019: \dfrac{£7.84+£8.21+£8.00+£8.50+£8.90+£8.40}{6}=£8.31
Mean for 2020:\dfrac{£9.50+£12.54+£12.05+£10.20+£9.10+£8.60}{6}=£10.33
Range for 2019: £8.90-£7.84=£1.06
Range for 2020: £12.54-£8.60=£3.94
Q5
Mrs Smith recorded the shoe sizes of her year 6 class:
3,\,\, 3.5,\,\, 5,\,\, 7,\,\, 3,\,\, 4,\,\, 5,\,\, 6,\,\, 2,\,\, 6.5,\,\, 4,\,\, 4.5,\,\, 5,\,\, 4,\,\, 5.5,\,\, 6,\,\, 4,\,\, 4.5,\,\, 5,\,\, 4\,\,Find the modal shoe size.
Answer: 4
Wrong Answers:
5
3.5
6
WORKING:
The shoe size of 4 is the most common size.
Q6
The list below shows the average amount (to the nearest pound) spent on fuel each week by some workers in an office.
£27, £12, £16, £19, £7, £30, £24, £11, £15Find the median amount spent on fuel.
Answer: £16
Wrong Answers:
£17.50
£19
£17.89
WORKING:
First we need to put the list in order:
£7, £11, £12, £15, £16, £19, £24, £27, £30So the median is the middle number of the above list, hence the median is £16.
Q7
Kevin records the ages of his whole family:
6,\,\, 13,\,\, 43, \,\, 65,\,\, 51,\,\, 22,\,\, 38,\,\, 78,\,\, 46,\,\, 44,\,\, 58,\,\, 10,\,\, 16,\,\, 14,\,\, 76,\,\, 89,\,\, 11,\,\, 15Find the mean age in his family to 2 decimal places.
Answer: 38.61
Wrong Answers:
40.5
34.75
36.58
WORKING:
6+13+43+65+51+22+38+78+46+44+58+10+16+14+76+89+11+15=695.
695\div18=38.61.
Q8
The table below shows the prices of flights to Majorca in a given week for two different airline companies.
By calculating the range for both airline companies, which company offers the most consistent prices?
Answer: Comfort Flight
Wrong Answer: Cheaper Jets
WORKING:
Range for Comfort Flight =£139-£94=£45
Range for Cheaper Jets =£92-£38=£54
Therefore Comfort Flight prices are more consistent as the range is lower.
Q9
The table below shows the mileage of ten cars from two different car garages.
Which garage sells cars with the lowest mileage?
Answer: Reverse the Price
Wrong Answer: Cheap Motors
WORKING:
Mean mileage of Cheap Motors =\dfrac{25+41+38+62+53+37+21+9+15+45}{10}=34.6 thousand = 34600.
Mean mileage of Reverse the Price =\dfrac{41+11+14+15+33+58+45+29+27+19}{10}=29.2 thousand = 29200.
Q10
The mean weight of a group of friends 71.5 kg.
The total weight for a group of friends is 858 kg.
How many friends are there in the group?
Answer: 12
Wrong Answers:
10
13
11
WORKING:
The method to find the mean of a set of data, we add up all the numbers in the data set and then divide by how many numbers there are.
So, the the number of friends =858\div71.5=12.