Question

select the correct answer from each drop-down menu.

james needs to clock a minimum of 9 hours per day at work. the data set records his daily work hours, which vary between 9 hours and 12 hours, for a certain number of days.

\\{9, 9.5, 10, 10.5, 10.5, 11, 11, 11.5, 11.5, 11.5, 12, 12\\}.

the median number of hours james worked is choose an answer. the skew of the distribution is choose an answer.

options for skew:
negative
positive
zero
zero with symmetry

Explanation:

Find the median of the data set

The ordered data set of work hours is:

$$ \{9, 9.5, 10, 10.5, 10.5, 11, 11, 11.5, 11.5, 11.5, 12, 12\} $$

The number of data points is \(n = 12\).
The median is the average of the 6th and 7th values:

$$ \text{Median} = \frac{11 + 11}{2} = 11 $$

Calculate the mean of the data set

The sum of the data points is:

$$ 9 + 9.5 + 10 + 10.5 + 10.5 + 11 + 11 + 11.5 + 11.5 + 11.5 + 12 + 12 = 130 $$

The mean is:

$$ \text{Mean} = \frac{130}{12} \approx 10.83 $$

Determine the skewness of the distribution

Comparing the mean and the median:

$$ \text{Mean} \approx 10.83 < \text{Median} = 11 $$

Since the mean is less than the median, the distribution is skewed to the left, which corresponds to a negative skew.

Answer:

Select the correct answer from each drop-down menu.

James needs to clock a minimum of 9 hours per day at work. The data set records his daily work hours, which vary between 9 hours and 12 hours, for a certain number of days.

$$ \{9, 9.5, 10, 10.5, 10.5, 11, 11, 11.5, 11.5, 11.5, 12, 12\} $$

The median number of hours James worked is <blank>11</blank>. The skew of the distribution is <blank>negative</blank>.