Question

the following data set represents the number of hours students from different classes spent on social media per week: \\(\\{1, 2, 4, 4, 4, 5, 5, 6, 6, 7, 8, 8, 12, 15, 25\\}\\).

use the drop-down menu to answer the following questions.

can this data set be represented by a normal curve?

what is the justification for your answer?

Explanation:

Analyze the distribution symmetry

The data set is:

$$ \{1, 2, 4, 4, 4, 5, 5, 6, 6, 7, 8, 8, 12, 15, 25\} $$

Calculate the median:

$$ \text{Median} = 6 \quad (\text{the 8th value}) $$

Calculate the mean:

$$ \text{Mean} = \frac{1+2+4+4+4+5+5+6+6+7+8+8+12+15+25}{15} = \frac{112}{15} \approx 7.47 $$

Determine skewness

Compare the mean and median:

$$ \text{Mean} \approx 7.47 > \text{Median} = 6 $$

The presence of large values on the right side (\(12, 15, 25\)) pulls the mean to the right, indicating a right-skewed distribution.

Evaluate suitability for a normal curve

A normal curve represents a symmetric, bell-shaped distribution where:

$$ \text{Mean} \approx \text{Median} \approx \text{Mode} $$

Since this data set is strongly skewed to the right, it cannot be represented by a normal curve.

Answer:

Question 1

No

Question 2

The data set is skewed to the right.