The weekly milk yields (in liters) of six dairy cows on a commercial farm were recorded as… — JAMB UTME

The weekly milk yields (in liters) of six dairy cows on a commercial farm were recorded as follows: $8$ , $10$ , $14$ , $16$ , $22$ , and $26$ . What is the median weekly milk yield for the cows?

A
14 liters
15 litersCevap
C
16 liters
D
17 liters

Cevap

15 liters

For an even number of observations (

n = 6

), the median is defined as the mean of the two middle values after arranging the dataset in order. The middle values in

8, 10, 14, 16, 22, 26

are

14

and

16

. Computing their average yields

\frac{14 + 16}{2} = 15

liters.

Adım Adım Çözüm

Arrange the data in ascending order and count the number of observations

Ordered dataset:

8, 10, 14, 16, 22, 26

. Total observations (

n

) =

6

(an even number).

The median requires ordered data. For an even number of observations, the median is the average of the two central terms.

Identify the two central observations

The 3rd term is

14

and the 4th term is

16

The central positions correspond to

\frac{n}{2} = 3\text{rd}

and

\frac{n}{2} + 1 = 4\text{th}

values.

Calculate the arithmetic average of the two central terms

\text{Median} = \frac{14 + 16}{2} = 15

liters.

Taking the midpoint of the two central values gives the exact median of the dataset.

Anahtar Kavram

Calculation of median for an even number of ungrouped observations

Tahmini Süre:45s

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

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