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Data Variability Measures

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Data Variability Measures worksheet preview

Data Variability Measures

Statistical charts and graphs illustration

📊 Part 1: Understanding Range

1. The heights (in cm) of Year 11 students are: 165, 172, 158, 180, 167, 175, 163, 169

a) Maximum height: _________ cm

b) Minimum height: _________ cm

c) Range = Maximum - Minimum = _________

2. Two cricket teams' scores over 6 matches:

Team A: 145, 167, 152, 159, 148, 161

Team B: 120, 180, 135, 175, 140, 170

a) Range for Team A: _________

b) Range for Team B: _________

c) Which team has more consistent scores? Explain:

3. What does a large range tell us about a data set?

The data values are close together

The data values are spread out

The data has a high mean

The data has many values

📈 Part 2: Standard Deviation Concepts

4. Temperature readings (°C) over a week: 18, 20, 19, 22, 17, 21, 19

Using a calculator or spreadsheet, find:

a) Mean temperature: _________ °C

b) Standard deviation: _________ °C (to 1 decimal place)

5. Two cities have the same mean temperature of 15°C but different standard deviations:

City X: Standard deviation = 2.1°C

City Y: Standard deviation = 8.5°C

Which city has more variable weather? _________

Explain your reasoning:

6. Match the standard deviation values to their descriptions:
Small standard deviation (e.g., 1.2)
Large standard deviation (e.g., 15.8)
Zero standard deviation
All data values are identical
Data values are very spread out
Data values are clustered near the mean

🎯 Part 3: Comparing Variability

7. Test scores for two classes:

Class A: Mean = 75%, Range = 30%, Standard deviation = 8.2%

Class B: Mean = 75%, Range = 18%, Standard deviation = 5.1%

Which statements are true? (Tick all that apply)

Both classes have the same average performance

Class A has more consistent scores

Class B has less variability in scores

Class A has a wider spread of scores

8. In your own words, explain why both range and standard deviation are useful for understanding data:

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