Core Chapter 12: Statistics

Question 1

State the 3 ways of measuring the centre of data

Answer 1

1) Mode:
- Discrete data: most frequently occurring value
- Grouped data: class with the highest frequency

2) Mean: arithmetic average
x̄ = Sum of all data values/No. of data values

3) Median: middle value of ordered data set
- Odd number of data values: (n+1/2) th value
- Even number of data values: average of the 2 middle values

Question 2

Choose the appropriate measurement of centre

Answer 2

Mode:
- Only takes into account most usual value
- Only takes common values into account
- Not affected by extreme values

Mean:
- Takes into account of all values
- Affected by extreme values

Median:
- Gives the halfway point of data
- Only takes middle values into account
- Not affected by extreme values

Question 3

Explain how frequency tables can be used to derive mode and mean

Answer 3

Frequency tables:
- Value column (x)
- Frequency column (f) –> mode/modal class
- Product column (xf)
Mean = Σxf/Σf

Question 4

Explain how frequency tables are modified to represent grouped data

Answer 4

Extra column with calculated midpoint/mid-interval value (used as x column)

Question 5

State the 4 ways of measuring the spread of data

Answer 5

1) Range: Difference between the maximum and minimum data value
Range = Max. value - Min. value

2) Interquartile Range: range of the middle half of the data
IQR = Q3-Q1

3) Variance (σ2)

4) Standard deviation (σ)

Question 6

Explain how box-and-whisker diagrams can be interpreted

Answer 6

• Minimum value: lower whisker
• Q1: left edge of box
• Q2: line in box
• Q3: right edge of box
• Maximum value: upper whisker
• Asterisks: outliers
• Symmetric distribution: whiskers of equal lengths and line in middle of box
• Negatively skewed: lower whisker longer than upper whisker and line closer to right side of box
• Positively skewed: upper whisker longer than lower whisker and line closer to left side of box

Question 7

Determine outliers

Answer 7

Calculate lower and upper boundaries:

Upper boundary: Q3 + 1.5xIQR
Lower boundary: Q1 - 1.5xIQR

Any data values larger or smaller than the boundaries are outliers

Question 8

Use cumulative frequency graphs to find percentiles

Answer 8

Q1: 25%
Q2: 50%
Q3: 75%