1. Billy belongs to a local walking club. He asked 35 people in the club which Welsh mountain they liked to walk up the most. He recorded the information shown below.
(a) Draw a bar chart to show Billy’s data. Use the square grid below. [6]
(b) Complete the following sentence. [1]
The difference between the number of people who liked walking up Cadair Idris and the number who liked walking up Pen y Fan is …………………… .
(c) Billy says,
“The modal choice of mountain is Pen y Fan.”
Explain why Billy is not correct. [1]
(d) Billy went for a walk up Pen y Gadair Fawr.
(i) Pen y Gadair Fawr is 800 metres high. Calculate the height of Pen y Gadair Fawr in feet. [2]
Use: 1 metre is 3·3 feet
Pen y Gadair Fawr is …………………… feet high.
(ii) The walk took Billy 3 hours and 45 minutes. He started his walk at 10:30 a.m. At what time did he finish his walk? Give your answer using the 24-hour clock. [2]
(iii) Look at the table below. It gives the temperature at 6 a.m. each day for a week in March at Pen y Gadair Fawr.
Day
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
Temperature (°C)
–2
0
1
3
4
3
–1
Use the information in the table above to complete the following statements. [4]
The day with the lowest temperature is ……………………
The range of these temperatures is ……………………
The median of these temperatures is ……………………
Mark scheme (a)
Scheme
Marks
Comments
(Pen y Fan 7) Snowdon 14, Cadair Idris 8, Cadair Berwyn 6
B2
May be seen or inferred from their bar chart or tallies (or other diagram/graph) If scale such as going up in 5s, 4s, or 3s are used, award B2 for frequencies that are implied to be correct if unambiguous.
Award B1 for either:
Two out of Snowdon (14), Cadair Idris (8) and Cadair Berwyn (6)
E.g. number of people or frequency and individual names of mountains. The names of mountains may be on the bars or anywhere within the base of the corresponding bar.
Uniform scale starting from zero on frequency axis
B1
Allow a frequency scale starting with 1 at the top of the first square to imply a scale starting with zero. Allow the numbers in the boxes as long as it is a uniform scale used and starts from zero.
All bars correct heights and same widths. The 4 bars can be in any order.
B2
FT their frequencies or tallies throughout if seen. If B0 awarded for no uniform scale, FT if an implied uniform scale has been applied or FT ‘their uniform scale’ If no scale, allow one square to represent 1. Allow bars to be joined. Allow different size gaps between bars.
Award B1 for any one of the following:
2 or 3 correct bars with correct frequencies
Correct heights with inconsistent widths
Correct heights with bars not complete
Vertical line graph drawn with correct heights
Implied correct heights of 2 or 3 bars when using a scale such as 2 squares are worth 5 and the heights are not quite accurate.
Mark scheme (b)
Scheme
Marks
Comments
(8 – 7 =) 1
B1
Allow -1 FT ‘their Cadair Idris’ – 7 or FT 7 – ‘their Cadair Idris’
Mark scheme (c)
Scheme
Marks
Comments
Reasonable explanation, e.g. ‘because the most popular is Snowdon’ ‘because that is not the most popular’ ‘because the modal is Snowdon’ ‘because Snowdon has the most amount of people’ ‘because Pen Y Fan was not the most picked’ ‘because Pen y Fan only had 7 whereas Snowdon had 14’ ‘because the majority picked Snowdon’ ‘because Snowdon was liked the most’
E1
FT ‘their bar chart’. Ignore spurious statements if correct statement also seen.
Allow: ‘because it’s Snowdon’ ‘because the modal is the most’ ‘because Snowdon had the most likes’ ‘because there are others with more’ ‘because Cadair Idris is one more’ ‘because Snowdon has more people with the highest amount’ ‘because Cadair Idris and Snowdon have more’ ‘no it is Snowdon because it’s not the biggest’ ’14 people chose the mode (whereas only 7 chose Pen Y Fan)’ ‘because Snowdon is the highest’
Do not allow: ‘because Cadair Berwyn is less than Pen Y Fan’ ‘because it’s (only) 7 for Pen Y Fan’ ‘because Pen Y Fan isn’t in the middle of the 4 mountains’ ‘because it’s not the middle or average number’ ‘because the modal is 14’
Mark scheme (d)
Scheme
Marks
Comments
(i) 800 × 3·3 2640 (feet)
M1 A1
This may be seen in stages eg 3·3 × 100 × 8
(ii) 10:30 + 3hrs 45 mins
M1
Sight of 2:15 or 13:75 or 14:15am implies M1 Allow 10(:)30 + 3(:)45 for M1 If using adding on methods, it must be a clear method to award M1 with 3 hours and 45 minutes clearly being added on.
14:15
A1
Allow 14:15pm but not 14:15am ‘Do not accept 2:15 with or without p.m or a.m)
(iii) Monday 6 (°C)
B1 B1
Allow -2(°C) as indication of Monday Award B0 for -6(°C) FT from ‘Sunday’ with answer of 5
Median = 1 (°C)
B2
Award B1 for: Numbers in order: -2, -1, 0, 1, 3, 3, 4 or reverse order
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