Enter each data set into the statistics calculator. make note of the histogram, mean, and median of each data set. a = {10, 12, 12, 6, 8, 5, 4, 10, 8, 10, 12, 12, 6} b = {8, 8, 8, 7, 9, 7, 9, 10, 6, 8} which statements are true about the data sets? check all that apply. set a is symmetrical. set b has the same mean and median. set b is right skewed. set a is left skewed. the median of set a is larger than the mean of set a.

In the following sets; set A has a median of 10 and a mean of 8.85 and a skewness of -0.3061. Therefore about set A, the median of set A is larger than the mean of set A, It is also skewed to the left since it has a negative skewness and hence not symmetrical (skewness is 0). 
 set B, the median is 8 and the mean is 8 and the skewness is zero. therefore; set B has the same median and mean, set B is symmetrical since it has a skewness of 0. It is not right skewed (positive skewness)

Skewed data set is non-symmetrical, and is biased over one side. For the given data sets, the true statements are:

Set B has the same mean and medianThe median of set A is larger than the mean of set A.What is symmetrical data set?

Data set which has symmetry in values vs frequency graph(histogram) for some vertical axis, is called symmetrical data set.

What is right skewed and left skewed data set?

When the data set is not symmetrical and its graph is leaning on some side(left side or right side), then such data set is called skewed data set(skewed left, or right, respectively).

Median of right skewed data is higher than symmetric data with same range, and vice versa for left skewed data(ie smaller median than symmetrical data).

For the symmetrical data(specially bell distribution), the mean, median and mode lie on same point(the point over which the vertical line of symmetry lies).

Arranging the data sets with their values to frequencies:

For set A:
4 1

5 1

6 2

8 2

10 3

12 4

For set B:

6 1

7 2

8 4

9 2

10 1

The histogram plotted for set A will be leaning on right, as frequency increases as value increases. Thus, it is right skewed.

The histogram plotted for set B will be symmetric about value 8, as frequency before value 8 and after value 8 are symmetric(see the pattern 1, 2, 4,2,1 )

And therefore, for the given data sets, the true statements are:

Set B has the same mean and medianThe median of set A is larger than the mean of set A.

Learn more about skewed distributions here:

link

7.6 m/s faster

Step-by-step explanation:

Speed of swimmer = 1.8 meters per second

The distance covered by runner = 200

Time of runner = 21.3 sec

We have to find the speed of the runner first so that we can compare with the speed of swimmer.

Speed = Distance/Time

=> 200/21.3

=> 9.4 m/s

So we have to find the difference between both speeds

Difference = 9.4 - 1.8

=> 7.6 m/s

So the runner was 7.6 m/s faster..