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

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 = ( \sum x)/(n)`

This implies that,


`\bar X = ( 12 + 18 + 22 + 24 + 24 + 32 + 46)/(7)`


`\bar X = (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 = (12 + 12)/(2) = 12`

The mean is


`\bar X = (4 + 5 + 11 + 11 + 12 + 12 + 13 + 14 + 14 + 18)/(10)`

.

`\bar X = (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 = (12 + 14)/(2) = 13`


The mean of this data set is

`\bar X = (4 + 5 + 9 + 12 + 14 + 18 + 22 + 26)/(8)`



`\bar X = (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 = (2 + 3)/(2) = 2.5`


The mean is

`\bar X= (1 + 1 + 1 + 2 + 2 + 3 + 3 + 4+ 5 + 6)/(10)`



`\bar X= (28)/(10) = 2.8`

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