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

sets b,c, and d are positive because they keep going up. The set a is the negative set

Answer 2

Positive skewed means, most values in data set are on the right of median.we call it right skewed distribution also.And, negatively skewed means, there are more values in data set are which are in the left of median or mean.These distribution are also called left skewed.

Arranging the values in data set in ascending order

Set A: {12,14,18,22, 24,32, 46,} , median=22,as number of observation is odd. as, 46-22=24, 32-22=10, 24-22=2, 22-18=4, 22-14=8, 22-12=10}, difference is more on right ,so positively skewed.

Set B: {4, 5,11,11,12,12,13,14,14,18} , median
`=(12+12)/(2)=12`, 18-12=6, 12-4=8, 12-11=1, 14-12=2, 13-12=1, Difference is more towards left, so negatively skewed.

Set C: {4,5, 9, 12, 14,18,22, 26} , Median
`=(12+14)/(2)=13`, 13-4=9, 26-13=13, Skewed on right, as difference between median and end values are more towards right.

Set D: {1, 1, 1, 2, 2, 3, 3, 4, 5, 6}, Median
`=(2+3)/(2)=2.5`, as 2.5-1=1.5, 6- 2.5=3.5, Skewed on right, as difference between median and end values are more towards right.

The sets that show a positive skew are sets A,C,D.

The sets that show a negative skew are sets B.