Five numbers 3, 7, 8, x, and 12 are arranged in ascending order, where x > 8. If the mean … — JAMB UTME

Five numbers $3, 7, 8, x,$ and $12$ are arranged in ascending order, where $x > 8$ . If the mean of the data set is equal to its median, what is the value of $x$ ?

$10$ Cevap
B
$5$
C
$14$
D
$18$

Cevap

The value of

x

10

For five numbers arranged in ascending order with

x > 8

, the middle position (3rd value) is

8

, so the median is

8

. Summing all five values gives

3 + 7 + 8 + 12 + x = 30 + x

. Equating the mean

\frac{30 + x}{5}

to the median

8

yields

30 + x = 40

, which gives

x = 10

Adım Adım Çözüm

Determine the median of the ordered data set.

Since there are

5

numbers arranged in ascending order (

3, 7, 8, x, 12

) with

x > 8

, the median is the middle (3rd) number, which is

8

For an odd count of data points

n = 5

, the median position is

\frac{5+1}{2} = 3

Formulate the expression for the arithmetic mean.

\text{Mean} = \frac{3 + 7 + 8 + 12 + x}{5} = \frac{30 + x}{5}

The mean of an ungrouped data set is the sum of all values divided by the total number of items.

Equate the mean to the median and solve for

x

\begin{align*} \frac{30 + x}{5} &= 8 \\ 30 + x &= 40 \\ x &= 10 \end{align*}

The question specifies that the mean of the data set is equal to its median.

Anahtar Kavram

Measures of Central Tendency for Ungrouped Data

Tahmini Süre:1m 30s

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