Data Variability Measures

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Statistical charts and graphs illustration

📊 Part 1: Understanding Variability

1. Two rugby teams both score an average of 24 points per game. Which statement is most accurate?

Both teams are equally consistent

We need to know their variability to compare consistency

The team with higher total points is more consistent

Average points tell us everything we need to know

2. The range of a data set tells us:

The average value

The difference between the highest and lowest values

How many data points there are

The most common value

3. Standard deviation measures:

The middle value in a data set

The total of all values

The average distance of data points from the mean

The number of values above the mean

4. A data set with a smaller standard deviation is:

More spread out

More consistent/clustered around the mean

Always larger in size

Less reliable

🔢 Part 2: Calculating Variability Measures

5. Calculate the range and standard deviation for the daily temperatures (°C) in Auckland last week: 18, 22, 19, 25, 21, 20, 23

Step 1: Order the data: _________________________________

Step 2: Calculate the range: Highest value - Lowest value = _____ - _____ = _____°C

Step 3: Calculate the mean: Sum ÷ Number of values = _____ ÷ 7 = _____°C

Step 4: Standard deviation = _____ °C (show working above)

6. A bakery records the number of pies sold each day: 45, 52, 48, 61, 44, 50, 55

Range = _____ pies

Mean = _____ pies

Standard deviation = _____ pies

🎯 Part 3: Interpretation and Application

7. Two cricket batsmen have these scores over 6 matches:

Player A: 45, 47, 46, 44, 48, 46 (Mean = 46, Standard deviation = 1.4)

Player B: 52, 38, 49, 41, 55, 41 (Mean = 46, Standard deviation = 6.8)

Which player is more consistent? _______________

Explain your reasoning:

8. A weather station records rainfall (mm) for two months:

January: Range = 25mm, Standard deviation = 8.2mm

February: Range = 45mm, Standard deviation = 15.1mm

Which month had more predictable rainfall? Explain using statistical terminology:

9. Extension Challenge: If you removed the highest and lowest values from a data set, how would this likely affect the range and standard deviation?

10. Real-world Application: Describe a situation where knowing the variability of data would be more important than knowing just the average:

Data Variability Measures

Data Variability Measures

📊 Part 1: Understanding Variability

🔢 Part 2: Calculating Variability Measures

🎯 Part 3: Interpretation and Application

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