SET A
The elements of this set are,
[tex]32,12,24,46,18,22,24[/tex]
We arrange this data set in ascending order to get,
[tex]12,18,22,24,24,32,46[/tex]
The median for this data set is
[tex]median = 24[/tex]
The mean for this data set can be calculated using the formula,
[tex]\bar X = \frac{ \sum x}{n} [/tex]
This implies that,
[tex]\bar X = \frac{ 12 + 18 + 22 + 24 + 24 + 32 + 46}{7} [/tex]
[tex]\bar X = \frac{154}{7} = 22[/tex]
This data set is negatively skewed because the mean is less than the median.
SET B
This set contains the elements,
[tex]4, 12, 11, 14, 11, 5, 12, 13, 18, 14[/tex]
We arrange the elements of this set in ascending order to obtain,
[tex]4,5,11,11,12,12,13,14,14,18[/tex]
The median for this data set is,
[tex]median = \frac{12 + 12}{2} = 12[/tex]
The mean is
[tex] \bar X = \frac{4 + 5 + 11 + 11 + 12 + 12 + 13 + 14 + 14 + 18}{10} [/tex]
.
[tex]\bar X = \frac{114}{10} = 11.4[/tex]
This data set is negatively skewed because the mean I'd less than the median.
SET C
The set C has elements,
[tex]5, 4, 9, 12, 14, 26, 22, 18[/tex]
We arrange this set in ascending order to get,
[tex]4,5,9,12,14,18,22,26[/tex]
The median of this data set is
[tex]median = \frac{12 + 14}{2} = 13[/tex]
The mean of this data set is
[tex]\bar X = \frac{4 + 5 + 9 + 12 + 14 + 18 + 22 + 26}{8} [/tex]
[tex]\bar X = \frac{110}{8} = 13.75[/tex]
This is a positively skewed distribution because the mean is greater than the median
SET D
The elements of this set are
[tex]1, 1, 1, 2, 2, 3, 3, 4, 5, 6[/tex]
The median of this data set is
[tex]median = \frac{2 + 3}{2} = 2.5[/tex]
The mean is
[tex]\bar X= \frac{1 + 1 + 1 + 2 + 2 + 3 + 3 + 4+ 5 + 6}{10} [/tex]
[tex]\bar X= \frac{28}{10} = 2.8[/tex]
This data set is positively skewed because the mean is greater than the median.
