Question

Question 13 B0/2 peso We will rank the y-values of the following data set -2 y -4.5 8.5 -6 1.5 -1.4 0 0.8 2.5 4.6 The scatterplot of the data looks like this MacBook Pro

Answer 1

Here, x and y values are given.

The rank of x values (i.e. x-rank) are also given.

Now, we have to know the rank of y values (i.e. y-rank).

Basically, rank is the ordinal number of a value in a list arranged in a specified order (either increasing or decreasing).

Here, in this problem, x values are arranged in increasing order and then they have been given ranks i.e. the lesser the value of x, the lesser the rank.

That means the least value of x (-2) has the 1st rank as it is the least one among the others, the second value of x (-0.8) has the 2nd rank as it is greater than the least value (-2) but less than all the other values (except -2), the third value of x (0) has the 3rd rank as it is greater than -2 and -0.8 but less than 0.8, 2.5 and 4.6. So, in this way the rank has been given.

Now, come to the y values, the least value is -13.6. So obviously it's rank will be 1.

-6 is the value which is less than all the values (except -13.6), but only greater than -13.6. So, the value -6 will be in the second position i.e. it's rank will be 2.

-4.5 is the value which is less than all the values (except -13.6 and -6), but greater than -13.6 and -6. So, the value -4.5 will be in the third position i.e. it's rank will be 3.

-1.4 is the value which is less than 8.5 and 1.5, but greater than -13.6, -6 and -4.5. So, the value -1.4 will be in the fourth position i.e. it's rank will be 4.

1.5 is the value which is less than 8.5, but greater than -13.6, -6, -4.5 and -1.4. So, the value 1.5 will be in the fifth position i.e. it's rank will be 5.

8.5 is the highest value among all the y-values, i.e. 8.5 is greater than all the values -13.6, -6, -4.5, -1.4 and 1.5. So, the value 8.5 will be in the sixth position i.e. it's rank will be 6.

We have the rankings of y-values and in the following table, the rankings are given.

x	y	x-rank	y-rank
-2	-4.5	1	3
-0.8	8.5	2	6
0	-6	3	2
0.8	1.5	4	5
2.5	-1.4	5	4
4.6	-13.6	6	1