Question

select the correct answer from each drop-down menu.

determine the best measure of center and the skew of the data distribution.

\\{23, 29, 12, 14, 27, 23, 23, 18, 23, 1, 7, 18, 43, 24, 28, 17, 32, 33, 38\\}

the value that best defines the central tendency of the distribution is choose an answer. the distribution exhibits a choose an answer skew.

Explanation:

Sort the data set and calculate the median

The given data set is:

$$ \{23, 29, 12, 14, 27, 23, 23, 18, 23, 1, 7, 18, 43, 24, 28, 17, 32, 33, 38\} $$

The number of data points is \(N = 19\).
Sorting the data in ascending order:

$$ 1, 7, 12, 14, 17, 18, 18, 23, 23, 23, 23, 24, 27, 28, 29, 32, 33, 38, 43 $$

The median is the \(10^{\text{th}}\) value (since \(\frac{19+1}{2} = 10\)):

$$ \text{Median} = 23 $$

Calculate the mean

Sum of the data points:

$$ \sum = 1 + 7 + 12 + 14 + 17 + 18 + 18 + 23 + 23 + 23 + 23 + 24 + 27 + 28 + 29 + 32 + 33 + 38 + 43 = 405 $$

The mean is:

$$ \text{Mean} = \frac{405}{19} \approx 21.32 $$

Determine the skewness and the best measure of center

Comparing the mean and median:

$$ \text{Mean} \approx 21.32 < \text{Median} = 23 $$

Since the mean is less than the median, the distribution exhibits a negative skew.
For a skewed distribution, the median is the best measure of central tendency.
Thus, the value that best defines the central tendency is the median, which is \(23\), and the skew is negative.

Answer:

Determine the best measure of center and the skew of the data distribution.

\(\{23, 29, 12, 14, 27, 23, 23, 18, 23, 1, 7, 18, 43, 24, 28, 17, 32, 33, 38\}\)

The value that best defines the central tendency of the distribution is <blank>23</blank>. The distribution exhibits a <blank>negative</blank> skew.