Five whole numbers are written in order. 4 6 х у
10
The mean and median of the five numbers are the same.
Work out the values of x and y.

x = 7

y = 8

Step-by-step explanation:

The following data were obtained from the question:

Data => 4, 6, х, y, 10

Mean = Median

x =?

y =?

Next, we shall determine the mean of the data. This can be obtained as follow:

Data => 4, 6, х, y, 10

Mean =?

Mean = summation of data / number of data

Mean = 4 + 6 + х + y + 10 / 5

Mean = 20 + х + y / 5

Next, we shall determine the median of the data. This can be obtained as follow:

Data => 4, 6, х, y, 10

Median =?

Median = the middle term of data

Median = x

Next, we shall equate the mean and median. This can be obtained as follow:

Mean = 20 + х + y / 5

Median = x

Mean = Median

20 + х + y / 5 = x

Cross multiply

20 + х + y = 5x

Collect like terms

20 + y = 5x – x

20 + y = 4x

Make y the subject

y = 4x – 20

Case 1

Let x = 7

y = 4x – 20

y = 4(7) – 20

y = 28 – 20

y = 8

Mean = 20 + х + y / 5

Mean = 20 + 7 + 8 / 5

Mean = 35/5

Mean = 7

Median = x

x = 7

Median = 7

Mean = median = x = 7

Case 2:

Let x = 8

y = 4x – 20

y = 4(8) – 20

y = 32 – 20

y = 12

We can see that y is 12 which means that the data (i.e 4, 6, х, y, 10) would become 4, 6, х, 10, y. But from the question, we were told that the data (i.e 4, 6, х, y, 10) is in order. Therefore if y is 12, the order would be altered.! And this is not acceptable.

From the above illustration, we can conclude that:

x = 7

y = 8

muyb ajo

step-by-step explanation:

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