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AQA GCSE · Question 09.4 · Statistical Measures and Calculations
Use calculations to confirm that there are no outliers in the new sample of 500 customers. You must show your working.
Use calculations to confirm that there are no outliers in the new sample of 500 customers. You must show your working.
How to approach this question
1. **Recall the rule for outliers**: An outlier is any data point that is more than 1.5 times the interquartile range (IQR) below the lower quartile (Q1) or above the upper quartile (Q3).
2. **State the values needed from the new sample**:
* Q1 = 1
* Q3 = 3
3. **Calculate the IQR**: IQR = Q3 - Q1 = 3 - 1 = 2.
4. **Calculate the lower boundary**:
* Formula: Q1 - (1.5 * IQR)
* Calculation: 1 - (1.5 * 2) = 1 - 3 = -2.
5. **Calculate the upper boundary**:
* Formula: Q3 + (1.5 * IQR)
* Calculation: 3 + (1.5 * 2) = 3 + 3 = 6.
6. **Compare with data**:
* The minimum value in the sample is 1. Is 1 < -2? No. So no low outliers.
* The maximum value in the sample is 5. Is 5 > 6? No. So no high outliers.
7. **Write a conclusion**: State that since no data points lie outside the calculated boundaries, there are no outliers.
Full Answer
From the new sample data (from 9.2/9.3):
Lower Quartile (Q1) = 1
Upper Quartile (Q3) = 3
Interquartile Range (IQR) = Q3 - Q1 = 3 - 1 = 2
**Check for low outliers:**
Lower boundary = Q1 - 1.5 * IQR
Lower boundary = 1 - 1.5 * 2 = 1 - 3 = -2.
The minimum value in the data is 1. Since 1 > -2, there are no low outliers.
**Check for high outliers:**
Upper boundary = Q3 + 1.5 * IQR
Upper boundary = 3 + 1.5 * 2 = 3 + 3 = 6.
The maximum value in the data is 5. Since 5 < 6, there are no high outliers.
Since there are no values below the lower boundary or above the upper boundary, there are no outliers in the new sample.
To check for outliers, we must first calculate the upper and lower boundaries for acceptable data points. The rule is that any point outside the range [Q1 - 1.5×IQR, Q3 + 1.5×IQR] is considered an outlier.
**Step 1: Find Q1, Q3, and IQR for the new sample.**
From the analysis in the previous parts:
- Lower Quartile (Q1) = 1
- Upper Quartile (Q3) = 3
- Interquartile Range (IQR) = Q3 - Q1 = 3 - 1 = 2
**Step 2: Calculate the lower boundary.**
Lower Boundary = Q1 - (1.5 × IQR)
Lower Boundary = 1 - (1.5 × 2) = 1 - 3 = -2
**Step 3: Calculate the upper boundary.**
Upper Boundary = Q3 + (1.5 × IQR)
Upper Boundary = 3 + (1.5 × 2) = 3 + 3 = 6
**Step 4: Compare with the data range.**
The data for the number of rewards ranges from a minimum of 1 to a maximum of 5.
- The minimum value (1) is greater than the lower boundary (-2).
- The maximum value (5) is less than the upper boundary (6).
**Conclusion:** Since all data points lie within the boundaries of -2 and 6, there are no outliers in the new sample.
Common mistakes
✗ Using the data from the old sample instead of the new one.
✗ Using an incorrect formula, e.g., Q1 - IQR or Q3 + IQR.
✗ Making a calculation error.
✗ Forgetting to write a final conclusion after doing the calculations.
Practice the full AQA GCSE Statistics Higher Tier Paper 1
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