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.

Explanation:

🆕 New Concept Discovered: Describing Data Distributions
Analyzing the center and shape of a data set.

Step 1: Find the median

The data set is already ordered from least to greatest:

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

Count the total number of data points (\(n\)):

$$ n = 12 $$

Since \(n\) is even, the median is the average of the two middle values (the \(6^{\text{th}}\) and \(7^{\text{th}}\) values):

• \(6^{\text{th}}\) value = \(11\)
• \(7^{\text{th}}\) value = \(11\)

Calculate the median:

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

Step 2: Determine the skewness

To find the skewness, we compare the mean and the median, or look at the concentration of the data points:

• Calculate the sum of the data:

$$ 9 + 9.5 + 10 + 10.5 + 10.5 + 11 + 11 + 11.5 + 11.5 + 11.5 + 12 + 12 = 129.5 $$

• Calculate the mean:

$$ \text{Mean} = \frac{129.5}{12} \approx 10.79 $$

Since the mean (\(\approx 10.79\)) is less than the median (\(11\)), the distribution is pulled to the left by the lower values. This indicates a negative skew (or skewed left).

Answer:

• The median number of hours James worked is 11.
• The skew of the distribution is negative (or skewed left).