Answer:
x = 7
y = 8
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