Statistics

Find the mean of 3, 5, 7, 9.

• A5
• B5.5
• C6✓
• D6.5

Answer: Mean = (3 + 5 + 7 + 9) ÷ 4 = 24 ÷ 4 = 6.

Find the median of 2, 4, 6, 8, 10.

• A4
• B6✓
• C7
• D8

Answer: Arrange in order: 2, 4, 6, 8, 10. The middle value is 6.

Find the mode of 1, 2, 2, 3, 4, 4, 4, 5.

• A2
• B3
• C4✓
• D5

Answer: The mode is the value that appears most often. 4 appears three times, which is more than any other.

Find the range of 5, 12, 8, 3, 15.

• A8.6
• B10
• C12✓
• D5

Answer: Range = highest - lowest = 15 - 3 = 12.

What is the median of 1, 3, 5, 7?

• A3
• B4✓
• C5
• D7

Answer: With 4 values, the median is the average of the 2nd and 3rd values: (3 + 5) ÷ 2 = 4.

A data set has 100 values. What is the position of the median?

• A51st
• B50th
• CBetween 50th and 51st✓
• D49th

Answer: With an even number of values, the median is between the (n/2)th and (n/2 + 1)th values. So between 50th and 51st.

Given: Mean = 50, Total of all values = 500. How many values are there?

• A5
• B10✓
• C50
• D500

Answer: Mean = Total ÷ Count. So Count = Total ÷ Mean = 500 ÷ 50 = 10.

A data set has mean 20. If you add a value of 20, what happens to the mean?

• AIt stays the same✓
• BIt increases
• CIt decreases
• DIt doubles

Answer: Adding a value equal to the mean doesn't change the mean.

The scores in a test are: 45, 50, 55, 60, 65, 70, 75. What is the range?

• A7
• B60
• C45
• D30✓

Answer: The range is the largest value minus the smallest: 75 − 45 = 30. There are 7 scores in the list and the middle one, the median, is 60, but neither of those is the range.

Find the mean of 10, 15, 20, 25, 30.

• A15
• B17.5
• C20✓
• D22.5

Answer: Mean = (10 + 15 + 20 + 25 + 30) ÷ 5 = 100 ÷ 5 = 20.

A frequency table shows: Value 1 appears 5 times, Value 2 appears 3 times, Value 3 appears 2 times. What is the mode?

• A1✓
• B2
• C3
• D5

Answer: The mode is the value with the highest frequency. Value 1 appears 5 times, which is the most.

In a frequency table, the mean is calculated using the formula: mean = Σ(fx) ÷ Σf. What does f represent?

• AFunction
• BFinal value
• CFrequency✓
• DFactor

Answer: In the formula Σ(fx) ÷ Σf, 'f' represents the frequency of each value.

A pie chart shows that 25% of students prefer maths. If there are 200 students, how many prefer maths?

• A25
• B50✓
• C75
• D100

Answer: 25% of 200 = 0.25 × 200 = 50.

A bar chart shows frequencies: 4, 6, 8, 10, 12. What is the total frequency?

• A8
• B30
• C40✓
• D50

Answer: Total = 4 + 6 + 8 + 10 + 12 = 40.

A scatter graph shows a strong positive correlation. What does this mean?

• AThe relationship is random
• BAs x increases, y increases✓
• CAs x increases, y decreases
• DThere is no relationship

Answer: A positive correlation means as one variable increases, the other also increases.

A stem-and-leaf plot shows: Stem 1 | Leaf 2, 3, 5; Stem 2 | Leaf 1, 4. What is the smallest value?

• A1
• B12✓
• C13
• D21

Answer: The smallest stem is 1, and the smallest leaf for that stem is 2. So the value is 12.

Which measure of central tendency is most affected by outliers?

• ARange
• BMedian
• CMean✓
• DMode

Answer: The mean is most affected by outliers because it uses all values in its calculation.

A data set has values: 5, 10, 15, 20, 25. If we add a value of 100, which statistic changes the least?

• AMedian✓
• BThe total of the values
• CMean
• DRange

Answer: Adding 100 changes the mean from 15 to about 29.2, the range from 20 to 95, and the total from 75 to 175. The median only moves from 15 to 17.5, which is the smallest change.

Given a frequency table with classes 0-10, 10-20, 20-30, 30-40, what is the midpoint of the class 20-30?

• A20
• B25✓
• C30
• D50

Answer: Midpoint = (20 + 30) ÷ 2 = 25.

The table shows the number of goals scored in 20 matches: 0 goals (4 matches), 1 goal (6 matches), 2 goals (5 matches), 3 goals (5 matches). What is the mean number of goals per match?

• A1.5 goals
• B6.2 goals
• C1.55 goals✓
• D7.75 goals

Answer: Total goals = (0x4) + (1x6) + (2x5) + (3x5) = 0 + 6 + 10 + 15 = 31. There are 20 matches, so the mean is 31 / 20 = 1.55 goals. Divide by the total frequency, not by the number of rows in the table.

Data: 2, 4, 6, 8, 10. What is the mean?

• A4
• B6✓
• C8
• D10

Answer: Mean = (2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6.

Data: 3, 5, 7, 9, 11. What is the median?

• A5
• B7✓
• C9
• D11

Answer: With 5 values, the median is the middle value (3rd): 7.

Data: 1, 2, 2, 3, 3, 3, 4. What is the mode?

• A2.5
• B3✓
• C2
• D4

Answer: The mode is the most frequently occurring value. 3 appears 3 times, so the mode is 3.

Data: 10, 20, 30, 40, 50. What is the range?

• A10
• B20
• C30
• D40✓

Answer: Range = highest - lowest = 50 - 10 = 40.

A grouped frequency table shows: 0-10 (5), 10-20 (8), 20-30 (6), 30-40 (1). What is the modal class?

• A10-20✓
• B0-10
• C30-40
• D20-30

Answer: The modal class is the class with the highest frequency. 10-20 has frequency 8, which is the highest.

A grouped frequency table shows: 0-10 (5), 10-20 (8), 20-30 (6), 30-40 (1). What is the estimate of the mean?

• A15
• B16.5✓
• C17
• D18

Answer: Use the class midpoints: 5×5 + 15×8 + 25×6 + 35×1 = 25 + 120 + 150 + 35 = 330. Total frequency = 5 + 8 + 6 + 1 = 20. Estimated mean = 330 ÷ 20 = 16.5.

Nine pupils took these times, in minutes, to finish a task: 12, 15, 9, 20, 11, 18, 14, 16, 10. What is the median time?

• A11 minutes
• B14 minutes✓
• C13.9 minutes
• D14.5 minutes

Answer: Put the times in order first: 9, 10, 11, 12, 14, 15, 16, 18, 20. With nine values the median is the 5th one, which is 14 minutes. Taking the middle of the unordered list gives 11, and 13.9 is the mean.

Two distributions are compared: A has mean 50, SD 5. B has mean 50, SD 10. Which is more spread out?

• AB✓
• BA
• CCannot determine
• DSame

Answer: A larger standard deviation indicates more spread. B has SD 10 > A's SD 5, so B is more spread out.

Two distributions are compared: A has mean 40, SD 5. B has mean 50, SD 5. Which has higher average?

• ACannot determine
• BA
• CSame
• DB✓

Answer: B has a higher mean (50 > 40), so B has a higher average.

A survey selects 100 people from a population of 5000, with every person equally likely to be chosen. What sampling method is this?

• ACluster
• BRandom✓
• CStratified
• DSystematic

Answer: In a simple random sample every member of the population has an equal chance of being selected. A stratified sample would first split the population into groups and sample each group in proportion to its size.

A stratified sample divides the population into groups (strata) and samples from each. Why is this useful?

• AIt's cheaper
• BIt's faster
• CIt ensures representation from each group✓
• DIt's always better

Answer: Stratified sampling ensures that each group in the population is represented in the sample.

A stem-and-leaf diagram uses the stem for tens and the leaves for units. Stem 2 has leaves 1, 4 and 7; stem 3 has leaves 0 and 5. What is the largest value shown?

• A30
• B35✓
• C27
• D5

Answer: The largest value uses the highest stem with its highest leaf: stem 3 with leaf 5 means 35. Reading only the stem gives 30, and 27 is the largest value on the lower stem.

A survey records favourite colours: red, blue, blue, green, blue. Which average can be used to describe this data?

• AMode✓
• BMean
• CMedian
• DRange

Answer: The data is categorical, so it cannot be added or put in numerical order. Only the mode, the most common value, can be found: blue appears three times. The range is a measure of spread rather than an average.

A frequency table shows the goals scored in each match: 1 goal in 5 matches, 2 goals in 3 matches and 3 goals in 2 matches. How many goals were scored in total?

• A10
• B17✓
• C6
• D30

Answer: Multiply each number of goals by its frequency and add: (1 × 5) + (2 × 3) + (3 × 2) = 5 + 6 + 6 = 17. Adding just the frequencies gives 10 and adding just the goal values gives 6.

A correlation coefficient r = 0.9 indicates what relationship?

• AStrong positive correlation✓
• BStrong negative correlation
• CWeak positive correlation
• DNo correlation

Answer: r = 0.9 is close to 1, indicating a strong positive correlation.