Question

The Mean of the following arrayed data, 5, 8, (3x − 1), (4x + 1), (3x + 7), is equal to its Median. Find the value of x.

Answer 1

Given:

The arrayed data set is 5, 8, (3x − 1), (4x + 1), and (3x + 7). The mean of this data set is equal to its median.

Formula:

Mean = Sum of observations / Number of observations

Median for odd number of observations = Value of the middle observation

Solution:

Number of observations (n) = 5  [Counting the given terms in the data set]

Median = 3x − 1  [Identifying the third and middle term of the arrayed data]

Sum of observations = 5 + 8 + (3x − 1) + (4x + 1) + (3x + 7)  [Adding all the given terms to find the total sum]

Sum of observations = 10x + 20  [Combining like terms to simplify the sum]

\[\therefore \text{Mean} = \frac{10x + 20}{5} \quad [\text{Dividing the total sum by the number of observations}]\]

\[\therefore \text{Mean} = 2x + 4 \quad [\text{Simplifying the fraction}]\]

2x + 4 = 3x − 1  [Equating the mean to the median as stated in the problem]

4 + 1 = 3x − 2x  [Transposing variable and constant terms to opposite sides]

x = 5  [Simplifying the expression to isolate x]

∴ x = 5