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25. The median of five numbers 10, x − 1,

Berikut ini adalah pertanyaan dari chelelelelllele pada mata pelajaran Matematika untuk jenjang Sekolah Menengah Pertama

25. The median of five numbers 10, x − 1, x − 5, x − 4 and x + 11 is 9. Find the mean of the 5 numbers.

Jawaban dan Penjelasan

Berikut ini adalah pilihan jawaban terbaik dari pertanyaan diatas.

The mean of those 5 numbers is 10.2.
(note: "." = decimal separator)
 

Problem

The median of five numbers 10, x - 1, x - 5, x - 4andx + 11is9. Find the mean of the 5 numbers.

Solution

Because there are five numbers, 9 should be the 3rd number.
Notice that x-5 < x-4 < x-1 < x+11. It means the first 3 numbers are x-5, x-4, and x-1. The number 10is greater than9 by 1, so 10 should be the 4th number. Hence, the sorted sequence is:

x-5, x-4, x-1, 10, x+11
\implies x-1 = 9
\therefore\ \ x = \bf10

The mean of those 5 numbers can be calculated in 2 ways.

1. Using pre-calculated numbers

By replacing xwith10, we get 5, 6, 9, 10, 21. The mean is:

\begin{aligned}\overline{x}&=\frac{5+6+9+10+21}{5}\\&=\frac{51}{5}\\\therefore\ \overline{x}&=\boxed{\:\bf10.2\:}\end{aligned}

2. Keeping x in calculation, and then substitute

The mean of x-5, x-4, x-1, 10, x+11 is:

\begin{aligned}\overline{x}&=\frac{x-5+x-4+x-1+10+x+11}{5}\\&=\frac{4x+11}{5}\\&\ \rightsquigarrow\left[\ x=10\ \right]\\&=\frac{4\times10\ +\ 11}{5}\\&=\frac{51}{5}\\\therefore\ \overline{x}&=\boxed{\:\bf10.2\:}\end{aligned}

\blacksquare

 

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Last Update: Fri, 16 Sep 22
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