Question

a researcher collects data on the daily screen time (in hours) of teenagers in a local community over one week. the recorded data is:

\\{1, 2, 2, 3, 3, 4, 4, 5, 15\\}.

use the drop-down arrow to choose the correct option.

can this data set be represented by a normal curve?

why or why not?

Explanation:

Analyze data symmetry and outliers

$$ \text{Data set: } \{1, 2, 2, 3, 3, 4, 4, 5, 15\} $$

$$ \text{Median} = 3 $$

$$ \text{Mean} = \frac{1+2+2+3+3+4+4+5+15}{9} = \frac{39}{9} \approx 4.33 $$

$$ \text{Outlier} = 15 \quad (\text{highly right-skewed}) $$

Evaluate normal distribution suitability

$$ \text{Normal distribution requirement: symmetric, bell-shaped, no extreme outliers.} $$

$$ \text{Since Mean } (4.33) > \text{ Median } (3) \text{ and } 15 \text{ is an extreme outlier, the data is strongly skewed to the right.} $$

$$ \text{Conclusion: No, it cannot be represented by a normal curve.} $$

Answer:

Question 1

No

Question 2

No, because the data set is skewed to the right due to the outlier of 15.