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Zorluk: OrtaMeasures of Central Tendency for Ungrouped Data

The mean of a set of 77 numbers arranged in ascending order is 1616. If the median of the set is 1616 and the mean of the smallest 33 numbers is 1111, what is the mean of the largest 33 numbers?

Cevap: 21

Cevap

The mean of the largest 3 numbers is 21.
For a set of 7 ordered numbers, the median is the 4th number, which is given as 16. The total sum of all 7 numbers is 7 × 16 = 112. The sum of the 3 smallest numbers is 3 × 11 = 33. Subtracting the 3 smallest numbers and the median from the total sum leaves the sum of the 3 largest numbers: 112 - 33 - 16 = 63. Dividing 63 by 3 gives a mean of 21.

Adım Adım Çözüm

1
Find the total sum of the set of 7 numbers
Sum = 7 × 16 = 112
The mean of a set is the total sum divided by the number of elements.
2
Determine the median value and the sum of the 3 smallest numbers
Median (4th number) = 16, Sum of 3 smallest = 3 × 11 = 33
For an ordered set of 7 numbers, the 4th number is the median, and the mean of the first 3 numbers gives their sum when multiplied by 3.
3
Calculate the sum of the 3 largest numbers
Sum of 3 largest = 112 - 33 - 16 = 63
The total sum is the sum of the 3 smallest numbers, the median (4th number), and the 3 largest numbers.
4
Compute the mean of the 3 largest numbers
Mean = 63 / 3 = 21
Dividing the sum of the 3 largest numbers by 3 gives their arithmetic mean.

Anahtar Kavram

Arithmetic Mean and Median of Ungrouped Data Subgroups
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Konular

Measures of Central Tendency for Ungrouped Data

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