The mean of five numbers arranged in ascending order is 28. The mean of the first three nu… — JAMB UTME

The mean of five numbers arranged in ascending order is $28$ . The mean of the first three numbers is $22$ , while the mean of the last three numbers is $36$ . Find the median of these five numbers.

Cevap: 34

Cevap

The median of the five numbers is

34

For five numbers ordered from smallest to largest (

x_1, x_2, x_3, x_4, x_5

), the median is the middle value

x_3

. The sum of all five numbers is

5 \times 28 = 140

. The sum of the first three numbers is

x_1 + x_2 + x_3 = 3 \times 22 = 66

, and the sum of the last three numbers is

x_3 + x_4 + x_5 = 3 \times 36 = 108

. Adding these two partial sums gives

(x_1 + x_2 + x_3 + x_4 + x_5) + x_3 = 66 + 108 = 174

. Substituting the overall sum of

140

into the equation yields

140 + x_3 = 174

, which simplifies to

x_3 = 34

Adım Adım Çözüm

Calculate the sum of all five numbers.

Sum of all 5 numbers is

5 \times 28 = 140

The total sum of a set of data equals the number of items multiplied by the mean.

Calculate the partial sums of the first three and last three numbers.

First three numbers sum to

3 \times 22 = 66

; last three numbers sum to

3 \times 36 = 108

Multiplying each sub-group mean by the count of numbers in that sub-group yields the sub-group sum.

Set up an equation relating the partial sums to the total sum and the median.

Adding the partial sums counts the third number (median) twice:

66 + 108 = 140 + \text{median}

In an ordered set of 5 numbers, the 3rd term is the median and is shared by both the first three and last three elements.

Solve for the median.

Median

= 174 - 140 = 34

Subtracting the total sum from the combined partial sums isolates the overlapping median value.

Anahtar Kavram

Measures of Central Tendency for Ungrouped Data (Relationship between sub-group means, total sum, and median in ordered data)

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