Question

7 observations are given as 15,12,18,15,18,x,y. (x,yellow are whole numbers).
1.write any 2 possible values of x, y if median of the data is x.
2.write any 2 possible values of x,y if the median is 15.​

Answer 1

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Answer 2

Answer:

The two sets of possible values of x and y each for the two given situations are found to be:

(i)- (a) x = 16, y = 18 or (b) x = 16, y = 19 for median being x.

(ii)- (a) x = 12, y = 18 or (b) x = 11, y = 19 for median being 15.

Step-by-step explanation:

The given set of seven observations are:

15, 12, 18, 15, 18, x, y

Now, we know that the median of the given set of observations is the middle value of the set of observations when it is arranged in an ascending order.

Now, there are a total of 7 observations, which means the fourth term will be its median.

(i) Median of the data is x:

Now ignoring the variables x and y and leaving them at the end, and arranging the remaining data in an ascending order, we get:

12, 15, 15, 18, 18, x, y

As the median is x, then the fourth term will be x, so, we get:

12, 15, 15, x, 18, 18, y

So, we'll choose x and y such that this order does not changes.

Thus, the possible values for x and y can be:

(a) x = 16, y = 18 or (b) x = 16, y = 19

(ii) Median of the data is 15:

Now ignoring the variables x and y and leaving them at the end, and arranging the remaining data in an ascending order, we get:

12, 15, 15, 18, 18, x, y

As the median is 15, then the fourth term will be 15, so, taking x at the start, we get:

x, 12, 15, 15, 18, 18, y

So, we'll choose x and y such that this order does not changes.

Thus, the possible values for x and y can be:

(a) x = 12, y = 18 or (b) x = 11, y = 19