Year 7 Statistics and probability: free practice test with answers

Sample statistics and probability questions with answers

Try each one before you open the answer.

1. Collecting and classifying data

   A random sample of $40$ students from a school of $800$ students was surveyed. $14$ of the sample said they ride a bike to school. Estimate how many students in the whole school ride a bike to school.

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   Key idea: A random sample should have about the same proportion as the whole population.

   1. Proportion in the sample $= \frac{14}{40}$.
   2. Estimate $= \frac{14}{40} \times 800 = 280$.

   Answer: $280$

2. Summarising data numerically

   The ages of players in a basketball squad are listed below.

   $$14, 15, 13, 16, 14, 15, 15, 14, 13, 16, 15, 14$$

   A stem-and-leaf plot is drawn with stems 13 and 14 and 15 and 16 (using tens and units). What is the median age of the squad?

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   Key idea: The median is the middle value when data is ordered. For an even number of values, average the two middle ones.

   1. Write all 12 ages in order: 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16
   2. Count the values: there are 12, which is even, so the median lies between the 6th and 7th values.
   3. The 6th value is $14$ and the 7th value is $15$.
   4. Median $= \dfrac{14 + 15}{2} = \dfrac{29}{2} = 14.5$

   Answer: $14.5$ years

3. Column graphs and dot plots

   A dot plot shows the number of books read by 10 students during the school holidays. The values are: 1, 1, 2, 2, 2, 3, 4, 4, 5, 6. Find the median number of books read.

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   Key idea: The median is the middle value when data is ordered. For an even number of values, average the two middle values.

   1. Write the 10 values in order: 1, 1, 2, 2, 2, 3, 4, 4, 5, 6
   2. With 10 values, the median is the average of the 5th and 6th values.
   3. The 5th value is $2$ and the 6th value is $3$.
   4. $\text{Median} = \frac{2 + 3}{2} = \frac{5}{2} = 2.5$ Answer: The median is $2.5$ books.

4. Line graphs

   A line graph shows the temperature during one day. The plotted points, joined by straight line segments, are: $6$ am $9°\text{C}$, $9$ am $14°\text{C}$, $12$ pm $21°\text{C}$, $3$ pm $23°\text{C}$, $6$ pm $17°\text{C}$.

   (a) Between which two consecutive readings did the temperature rise the most?

   (b) Use the graph to estimate the temperature at $4{:}30$ pm.

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   Key idea: The change between readings is found by subtraction. Halfway between two times on a straight segment, the value is halfway between the two readings.

   1. (a) Changes: $14 - 9 = 5$, $21 - 14 = 7$, $23 - 21 = 2$, $17 - 23 = -6$
   2. (a) The biggest rise is $7°\text{C}$, from $9$ am to $12$ pm
   3. (b) $4{:}30$ pm is halfway between $3$ pm and $6$ pm, so the reading is halfway between $23$ and $17$: $\dfrac{23 + 17}{2} = 20$

   Answer: (a) Between $9$ am and $12$ pm (b) $20°\text{C}$

5. Stem-and-leaf plots

   A stem-and-leaf plot displays the ages of 12 people at a community event.

   Stem	Leaves
   1	4 5 7 8
   2	0 3 3 6
   3	1 2 5 9

   The stem represents tens and the leaves represent ones. Find the range and the median age.

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   Key idea: Read each data value by combining its stem and leaf. The range is the difference between the maximum and minimum values. The median is the average of the two middle values when there are an even number of data values.

   1. List all 12 values in order: 14, 15, 17, 18, 20, 23, 23, 26, 31, 32, 35, 39
   2. Range: $39 - 14 = 25$
   3. With 12 values, the median is the average of the 6th and 7th values.
   4. The 6th value is $23$ and the 7th value is $23$.
   5. $\text{Median} = \frac{23 + 23}{2} = 23$ Answer: The range is $25$ and the median age is $23$ years.

6. Sector graphs and divided bar graphs

   In a survey of $40$ students, $10$ chose soccer as their favourite sport. What angle would the soccer sector have in a sector graph?

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   Key idea: Sector angle $= \dfrac{\text{frequency}}{\text{total}} \times 360°$.

   1. Fraction choosing soccer: $\dfrac{10}{40} = \dfrac{1}{4}$
   2. Angle: $\dfrac{1}{4} \times 360° = 90°$

   Answer: $90°$

7. Describing probability

   A standard six-sided die is rolled. Describe the chance of each event using one of: impossible, unlikely, even chance, likely, certain.

   (a) rolling a $7$ (b) rolling an even number (c) rolling a number less than $6$ (d) rolling a number from $1$ to $6$

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   Key idea: Compare the number of favourable outcomes with the $6$ possible outcomes.

   1. (a) No face shows $7$: $0$ out of $6$, impossible
   2. (b) $2, 4, 6$: $3$ out of $6$, even chance
   3. (c) 1, 2, 3, 4, 5: $5$ out of $6$, likely
   4. (d) All $6$ outcomes: certain

   Answer: (a) impossible (b) even chance (c) likely (d) certain

8. Theoretical probability in single-step experiments

   A standard six-sided die has faces numbered 1 to 6. List the sample space for one roll of the die, then find the probability of rolling a number greater than 4. Write your answer as a fraction, a decimal and a percentage.

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   Key idea: The sample space is the list of all possible outcomes. Probability = $\dfrac{\text{number of favourable outcomes}}{\text{total number of outcomes}}$

   1. List the sample space: $\{1, 2, 3, 4, 5, 6\}$. There are 6 equally likely outcomes.
   2. Identify the favourable outcomes (greater than 4): $\{5, 6\}$. There are 2 favourable outcomes.
   3. Write the probability as a fraction: $P(\text{greater than 4}) = \frac{2}{6} = \frac{1}{3}$
   4. Convert to a decimal: $\frac{1}{3} \approx 0.\overline{3}$
   5. Convert to a percentage: $\frac{1}{3} \times 100 \approx 33.3\%$

   Answer: $\dfrac{1}{3}$, approximately $0.\overline{3}$, approximately $33.3\%$

Free worksheets for this chapter

Worked examples and a free PDF with answers for each topic.

• Year 7 statistics worksheet
• Year 7 dot plots and stem-and-leaf plots worksheet
• Year 7 probability worksheet