Question

Consider these four data sets. Set A: {32, 12, 24, 46, 18, 22, 14} Set B: {4, 12, 11, 14, 11, 5, 12, 13, 18, 14} Set C: {5, 4, 9, 12, 14, 26, 22, 18} Set D: {1, 1, 1, 2, 2, 3, 3, 4, 5, 6} The sets that show a positive skew are sets . The sets that show a negative skew are sets

Answer 1

Answer:

Step-by-step explanation:

Set A: {32, 12, 24, 46, 18, 22, 14}

Mean =24 : Median =22:

Mean>Median hence positive skewed

Set B: {4, 12, 11, 14, 11, 5, 12, 13, 18, 14}

Mean =11.4 and median = 12

Mean <Median, hence negative skewed

Set C: {5, 4, 9, 12, 14, 26, 22, 18}

Mean=13.75 and median = 13

Mean >Median hence positive skewed

Set D: {1, 1, 1, 2, 2, 3, 3, 4, 5, 6}

Mean =2.8 Median = 2.5

Mean>Median Hence positive skewed

Answer 2

SET A

The elements of this set are,

$32,12,24,46,18,22,24$


We arrange this data set in ascending order to get,

$12,18,22,24,24,32,46$



The median for this data set is

$median = 24$


The mean for this data set can be calculated using the formula,

$\bar X = \frac{ \sum x}{n}$

This implies that,

$\bar X = \frac{ 12 + 18 + 22 + 24 + 24 + 32 + 46}{7}$

$\bar X = \frac{154}{7} = 22$
This data set is negatively skewed because the mean is less than the median.



SET B

This set contains the elements,

$4, 12, 11, 14, 11, 5, 12, 13, 18, 14$



We arrange the elements of this set in ascending order to obtain,

$4,5,11,11,12,12,13,14,14,18$

The median for this data set is,

$median = \frac{12 + 12}{2} = 12$

The mean is

$\bar X = \frac{4 + 5 + 11 + 11 + 12 + 12 + 13 + 14 + 14 + 18}{10}$

.
$\bar X = \frac{114}{10} = 11.4$

This data set is negatively skewed because the mean I'd less than the median.

SET C

The set C has elements,
$5, 4, 9, 12, 14, 26, 22, 18$

We arrange this set in ascending order to get,

$4,5,9,12,14,18,22,26$

The median of this data set is

$median = \frac{12 + 14}{2} = 13$


The mean of this data set is
$\bar X = \frac{4 + 5 + 9 + 12 + 14 + 18 + 22 + 26}{8}$


$\bar X = \frac{110}{8} = 13.75$


This is a positively skewed distribution because the mean is greater than the median


SET D


The elements of this set are

$1, 1, 1, 2, 2, 3, 3, 4, 5, 6$

The median of this data set is

$median = \frac{2 + 3}{2} = 2.5$


The mean is
$\bar X= \frac{1 + 1 + 1 + 2 + 2 + 3 + 3 + 4+ 5 + 6}{10}$


$\bar X= \frac{28}{10} = 2.8$

This data set is positively skewed because the mean is greater than the median.