Five packages delivered by a courier service have masses of 5\text{ kg}, 8\text{ kg}, 11\t… — JAMB UTME

Five packages delivered by a courier service have masses of $5\text{ kg}$ , $8\text{ kg}$ , $11\text{ kg}$ , $12\text{ kg}$ , and $14\text{ kg}$ . What is the mean deviation of the masses of these packages?

A
$0.0\text{ kg}$
$2.8\text{ kg}$ Cevap
C
$10.0\text{ kg}$
D
$14.0\text{ kg}$

Cevap

2.8\text{ kg}

The mean of the data set is

10\text{ kg}

. The distances of each data value from the mean are

5

2

1

2

, and

4

. The sum of these distances is

14

, and dividing by

5

yields a mean deviation of

2.8\text{ kg}

Adım Adım Çözüm

Calculate the arithmetic mean

(\bar{x})

of the dataset

\bar{x} = \frac{5 + 8 + 11 + 12 + 14}{5} = \frac{50}{5} = 10\text{ kg}

Mean deviation requires the central mean value as a reference point for all deviations.

Find the absolute deviation

|x - \bar{x}|

for each value in the dataset

|5 - 10| = 5, |8 - 10| = 2, |11 - 10| = 1, |12 - 10| = 2, |14 - 10| = 4

Mean deviation measures the average distance of values from the mean regardless of sign.

Sum the absolute deviations and divide by the sample size

(n = 5)

\text{Mean Deviation} = \frac{5 + 2 + 1 + 2 + 4}{5} = \frac{14}{5} = 2.8\text{ kg}

Dividing total absolute deviation by the total count yields the mean deviation.

Anahtar Kavram

Mean Deviation

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Konular

Bu konudan daha fazla soru