A set of six numbers arranged in ascending order is given as 3, 8, x, 14, y, 25. If the me… — JAMB UTME

A set of six numbers arranged in ascending order is given as $3, 8, x, 14, y, 25$ . If the median of the data set is $11$ and its arithmetic mean is $13$ , what is the value of $y$ ?

A
$17$
$20$ Answer
C
$22$
D
$16$

Answer

The value of

y

20

The median of an even number of values arranged in order is the average of the two central terms, which gives

\frac{x + 14}{2} = 11

, solving to

x = 8

. Since the mean of the six numbers is

13

, their total sum is

6 \times 13 = 78

. Adding all terms gives

3 + 8 + 8 + 14 + y + 25 = 58 + y = 78

, which yields

y = 20

Step-by-Step Solution

Find the value of

x

using the median of the six ordered numbers.

\frac{x + 14}{2} = 11 \implies x + 14 = 22 \implies x = 8

For an even number of observations (

n = 6

), the median is the average of the 3rd term (

x

) and 4th term (

14

Calculate the required total sum of all six numbers using the given mean.

\text{Total Sum} = 6 \times 13 = 78

The mean of

n

numbers is equal to the sum of the numbers divided by

n

Sum all six terms and solve for

y

3 + 8 + 8 + 14 + y + 25 = 78 \implies 58 + y = 78 \implies y = 20

Substitute

x = 8

into the dataset and set the sum of all elements equal to

78

Key Concept

Measures of Central Tendency for Ungrouped Data

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