Exam Questions — Statistics
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2 marks
Foundation
Edexcel
Statistics
\begin{aligned} &\text{10 children were asked which day of the week is their favourite.}\\ &\text{Saturday, Friday, Saturday, Sunday, Saturday, Friday, Saturday, Sunday, Friday, Saturday.} \end{aligned}
- a) \begin{aligned} &\text{Complete the frequency table:}\\[2mm] &\begin{array}{|l|c|c|}\hline \textbf{Day} & \textbf{Tally} & \textbf{Frequency}\\\hline \text{Saturday} & & \\ \text{Friday} & & \\ \text{Sunday} & & \\\hline \end{array} \end{aligned} (1 mark)
- b) \[\text{Which day is the mode?}\] (1 mark)
a)
Answer:
\begin{aligned} &\begin{array}{|l|c|c|}\hline \textbf{Day} & \textbf{Tally} & \textbf{Frequency}\\\hline \text{Saturday} & \texttt{|||||} & 6\\ \text{Friday} & \texttt{|||} & 3\\ \text{Sunday} & \texttt{|} & 1\\\hline \end{array} \end{aligned}
Solution:
\begin{aligned} &\text{Saturday = 6, Friday = 3, Sunday = 1.}\end{aligned}
b)
Answer:
\[\text{Saturday}\]
Solution:
\[\text{Saturday has the highest frequency (6).}\]
2 marks
Foundation
Edexcel
Statistics
\begin{aligned} &\text{12 pupils were asked how many sisters they have.}\\ &0,1,0,2,1,1,0,2,1,0,1,0. \end{aligned}
- a) \begin{aligned} &\text{Complete the frequency table:}\\[2mm] &\begin{array}{|c|c|c|}\hline \textbf{No. of sisters} & \textbf{Tally} & \textbf{Frequency}\\\hline 0 & & \\ 1 & & \\ 2 & & \\\hline \end{array} \end{aligned} (1 mark)
- b) \[\text{Write down the mode.}\] (1 mark)
a)
Answer:
\begin{aligned} &\begin{array}{|c|c|c|}\hline \textbf{No. of sisters} & \textbf{Tally} & \textbf{Frequency}\\\hline 0 & \texttt{|||||} & 5\\ 1 & \texttt{|||||} & 5\\ 2 & \texttt{||} & 2\\\hline \end{array} \end{aligned}
Solution:
\begin{aligned} &\text{0 appears 5 times, 1 appears 5 times, 2 appears 2 times.}\end{aligned}
b)
Answer:
\[\text{0 and 1}\]
Solution:
\[\text{Both 0 and 1 occur 5 times, so the data is bimodal.}\]
2 marks
Foundation
Edexcel
Statistics
\begin{aligned} &\text{15 people were asked which drink they prefer.}\\ &\text{tea, coffee, tea, juice, tea, water, coffee, tea, juice, tea,}\\ &\text{coffee, juice, tea, water, coffee.} \end{aligned}
- a) \begin{aligned} &\text{Complete the frequency table:}\\[2mm] &\begin{array}{|l|c|c|}\hline \textbf{Drink} & \textbf{Tally} & \textbf{Frequency}\\\hline \text{Tea} & & \\ \text{Coffee} & & \\ \text{Juice} & & \\ \text{Water} & & \\\hline \end{array} \end{aligned} (1 mark)
- b) \[\text{What is the mode?}\] (1 mark)
a)
Answer:
\begin{aligned} &\begin{array}{|l|c|c|}\hline \textbf{Drink} & \textbf{Tally} & \textbf{Frequency}\\\hline \text{Tea} & \texttt{|||||} & 6\\ \text{Coffee} & \texttt{|||} & 3\\ \text{Juice} & \texttt{|||} & 3\\ \text{Water} & \texttt{||} & 2\\\hline \end{array} \end{aligned}
Solution:
\begin{aligned} &\text{Tea = 6, Coffee = 3, Juice = 3, Water = 2.}\end{aligned}
b)
Answer:
\[\text{Tea}\]
Solution:
\[\text{Tea has the highest frequency, 6.}\]
2 marks
Foundation
Edexcel
Statistics
\begin{aligned} &\text{20 children were asked which season they like best.}\\ &\text{summer, winter, summer, autumn, summer, spring, autumn, summer, winter, spring,}\\ &\text{summer, autumn, summer, winter, spring, summer, autumn, summer, winter, spring.} \end{aligned}
- a) \begin{aligned} &\text{Complete the frequency table:}\\[2mm] &\begin{array}{|l|c|c|}\hline \textbf{Season} & \textbf{Tally} & \textbf{Frequency}\\\hline \text{Summer} & & \\ \text{Winter} & & \\ \text{Autumn} & & \\ \text{Spring} & & \\\hline \end{array} \end{aligned} (1 mark)
- b) \[\text{What is the mode?}\] (1 mark)
a)
Answer:
\begin{aligned} &\begin{array}{|l|c|c|}\hline \textbf{Season} & \textbf{Tally} & \textbf{Frequency}\\\hline \text{Summer} & \texttt{||||||||} & 8\\ \text{Winter} & \texttt{||||} & 4\\ \text{Autumn} & \texttt{||||} & 4\\ \text{Spring} & \texttt{||||} & 4\\\hline \end{array} \end{aligned}
Solution:
\[\text{Summer occurs 8 times, most frequent.}\]
b)
Answer:
\[\text{Summer}\]
Solution:
\[\text{Summer is the most common choice.}\]
2 marks
Foundation
Edexcel
Statistics
\begin{aligned} &\text{A class of 16 pupils were asked how many brothers they have.}\\ &0,1,2,0,1,2,0,0,1,2,0,1,0,2,1,0. \end{aligned}
- a) \begin{aligned} &\text{Complete the frequency table:}\\[2mm] &\begin{array}{|l|c|c|}\hline \textbf{No. of brothers} & \textbf{Tally} & \textbf{Frequency}\\\hline 0 & & \\ 1 & & \\ 2 & & \\\hline \end{array} \end{aligned} (1 mark)
- b) \[\text{What is the mode?}\] (1 mark)
a)
Answer:
\begin{aligned} &\begin{array}{|l|c|c|}\hline \textbf{No. of brothers} & \textbf{Tally} & \textbf{Frequency}\\\hline 0 & \texttt{||||||} & 6\\ 1 & \texttt{|||||} & 5\\ 2 & \texttt{|||||} & 5\\\hline \end{array} \end{aligned}
Solution:
\begin{aligned} &0=6,\;1=5,\;2=5.\end{aligned}
b)
Answer:
\[0\]
Solution:
\[ \text{0 occurs 6 times, the highest frequency.} \]
2 marks
Foundation
Edexcel
Statistics
\begin{aligned} &\text{18 students were asked what colour pen they use most.}\\ &\text{blue, black, blue, black, blue, red, blue, black, blue, green,}\\ &\text{blue, black, red, blue, black, green, black, blue.} \end{aligned}
- a) \begin{aligned} &\text{Complete the frequency table:}\\[2mm] &\begin{array}{|l|c|c|}\hline \textbf{Colour} & \textbf{Tally} & \textbf{Frequency}\\\hline \text{Blue} & & \\ \text{Black} & & \\ \text{Red} & & \\ \text{Green} & & \\\hline \end{array} \end{aligned} (1 mark)
- b) \[\text{Write down the mode.}\] (1 mark)
a)
Answer:
\begin{aligned} &\begin{array}{|l|c|c|}\hline \textbf{Colour} & \textbf{Tally} & \textbf{Frequency}\\\hline \text{Blue} & \texttt{|||||||||} & 9\\ \text{Black} & \texttt{||||||} & 6\\ \text{Red} & \texttt{||} & 2\\ \text{Green} & \texttt{|} & 1\\\hline \end{array} \end{aligned}
Solution:
\begin{aligned} &\text{Blue = 9, Black = 6, Red = 2, Green = 1.}\end{aligned}
b)
Answer:
\[\text{Blue}\]
Solution:
\[\text{Blue has the highest frequency.}\]
2 marks
Foundation
Edexcel
Statistics
\begin{aligned} &\text{Miss Green asked 12 pupils which sport they like best.}\\ &\text{football, tennis, football, basketball, football, tennis,}\\ &\text{football, basketball, tennis, football, tennis, football.} \end{aligned}
- a) \begin{aligned} &\text{Complete the frequency table:}\\[2mm] &\begin{array}{|l|c|c|}\hline \textbf{Sport} & \textbf{Tally} & \textbf{Frequency}\\\hline \text{Football} & & \\ \text{Tennis} & & \\ \text{Basketball} & & \\\hline \end{array} \end{aligned} (1 mark)
- b) \[\text{Which sport is the mode?}\] (1 mark)
a)
Answer:
\begin{aligned} &\begin{array}{|l|c|c|}\hline \textbf{Sport} & \textbf{Tally} & \textbf{Frequency}\\\hline \text{Football} & \texttt{||||||} & 6\\ \text{Tennis} & \texttt{||||} & 4\\ \text{Basketball} & \texttt{||} & 2\\\hline \end{array} \end{aligned}
Solution:
\begin{aligned} &\text{Football = 6, Tennis = 4, Basketball = 2.}\end{aligned}
b)
Answer:
\[\text{Football}\]
Solution:
\[\text{Football is the most frequent answer.}\]
2 marks
Foundation
Edexcel
Statistics
\begin{aligned} &\text{20 children were asked what pet they have.}\\ &\text{dog, cat, dog, rabbit, cat, dog, fish, dog, rabbit, cat,}\\ &\text{dog, fish, cat, rabbit, dog, fish, dog, rabbit, cat, dog.} \end{aligned}
- a) \begin{aligned} &\text{Complete the frequency table:}\\[2mm] &\begin{array}{|l|c|c|}\hline \textbf{Pet} & \textbf{Tally} & \textbf{Frequency}\\\hline \text{Dog} & & \\ \text{Cat} & & \\ \text{Rabbit} & & \\ \text{Fish} & & \\\hline \end{array} \end{aligned} (1 mark)
- b) \[\text{What is the mode?}\] (1 mark)
a)
Answer:
\begin{aligned} &\begin{array}{|l|c|c|}\hline \textbf{Pet} & \textbf{Tally} & \textbf{Frequency}\\\hline \text{Dog} & \texttt{||||||||} & 8\\ \text{Cat} & \texttt{||||} & 4\\ \text{Rabbit} & \texttt{||||} & 4\\ \text{Fish} & \texttt{|||} & 3\\\hline \end{array} \end{aligned}
Solution:
\begin{aligned} &\text{Dog = 8, Cat = 4, Rabbit = 4, Fish = 3.}\end{aligned}
b)
Answer:
\[\text{Dog}\]
Solution:
\[\text{Dog occurs 8 times, the most frequent.}\]
2 marks
Foundation
Edexcel
Statistics
\begin{aligned} &\text{15 students were asked how they travel to school.}\\ &\text{walk, bus, walk, car, car, walk, bus, bus, car, walk, car, bus, walk, car, bus.} \end{aligned}
- a) \begin{aligned} &\text{Complete the frequency table:}\\[2mm] &\begin{array}{|l|c|c|}\hline \textbf{Travel} & \textbf{Tally} & \textbf{Frequency}\\\hline \text{Walk} & & \\ \text{Bus} & & \\ \text{Car} & & \\\hline \end{array} \end{aligned} (1 mark)
- b) \[\text{What is the mode?}\] (1 mark)
a)
Answer:
\begin{aligned} &\begin{array}{|l|c|c|}\hline \textbf{Travel} & \textbf{Tally} & \textbf{Frequency}\\\hline \text{Walk} & \texttt{|||||} & 5\\ \text{Bus} & \texttt{|||||} & 5\\ \text{Car} & \texttt{|||||} & 5\\\hline \end{array} \end{aligned}
Solution:
\begin{aligned} &\text{Walk = 5, Bus = 5, Car = 5.}\end{aligned}
b)
Answer:
\[\text{Walk, Bus and Car (all equal)}\]
Solution:
\[\text{Each occurs 5 times.}\]
2 marks
Foundation
Edexcel
Statistics
\begin{aligned} &\text{A teacher asked 20 students which fruit they like best.}\\ &\text{apple, banana, apple, orange, apple, banana, grape, apple, orange, banana,}\\ &\text{apple, grape, banana, apple, orange, apple, banana, grape, apple, orange.} \end{aligned}
- a) \begin{aligned} &\text{Complete the frequency table:}\\[2mm] &\begin{array}{|l|c|c|}\hline \textbf{Fruit} & \textbf{Tally} & \textbf{Frequency}\\\hline \text{Apple} & \;&\;\\ \text{Banana} & \;&\;\\ \text{Orange} & \;&\;\\ \text{Grape} & \;&\;\\\hline \end{array} \end{aligned} (1 mark)
- b) \[\text{Write down the mode.}\] (1 mark)
a)
Answer:
\begin{aligned} &\begin{array}{|l|c|c|}\hline \textbf{Fruit} & \textbf{Tally} & \textbf{Frequency}\\\hline \text{Apple} & \texttt{||||||||} & 8\\ \text{Banana} & \texttt{|||||} & 5\\ \text{Orange} & \texttt{||||} & 4\\ \text{Grape} & \texttt{|||} & 3\\\hline \end{array} \end{aligned}
Solution:
\begin{aligned} &\text{Counts: Apple }8,\; \text{Banana }5,\; \text{Orange }4,\; \text{Grape }3.\end{aligned}
b)
Answer:
\[\text{Apple}\]
Solution:
\[\text{Apple has the greatest frequency (}8\text{).}\]