中央値 and 平均: the middle ordered value and the arithmetic mean
Find the median of an odd number of ordered values and compare it with adding all values and dividing to obtain an arithmetic mean.
The middle after ordering
中央値, read ちゅうおうち, means the median after values are ordered by size. 値を小さい順に並べて中央値を求めた。 says that the values were ordered from smallest to largest and the median was found.
The three values 三、十、一 become 一、三、十 when ordered. The middle value is three, not the ten in the original written order.
Add all values and divide by their count
To obtain 平均, read へいきん, as an arithmetic mean, add the values and divide by the number of observations. One, three, and ten total fourteen, so the mean is fourteen divided by three.
The median three differs from that mean. The same data can give different results depending on whether the method uses the middle position or the sum.
Check ordering and the reported result
平均値と中央値を比べました。 reports comparing the mean and median. It does not already establish that they are equal.
This example uses an odd number of observations. Do not translate 中央値 as a spatial middle seat or choose the middle written number without ordering by value.
Is ten the 中央値 of the three values 十、一、三?
Show the answer and why
No. Ordering them as one, three, and ten gives three as the middle value. Check numerical order rather than the order initially written.