The masses, in kilograms, of five wooden crates stored in a warehouse are 3, 7, 8, 10, and… — JAMB UTME

The masses, in kilograms, of five wooden crates stored in a warehouse are $3$ , $7$ , $8$ , $10$ , and $12$ . What is the variance of the masses of these crates?

$9.2$ Cevap
B
$2.4$
C
$11.5$
D
$46.0$

Cevap

The variance of the masses is

9.2

The mean of the numbers is

8

. The squared deviations are

25, 1, 0, 4,

and

16

. The sum of these squared deviations is

46

. Dividing by the count of numbers (

5

) gives

9.2

Adım Adım Çözüm

Calculate the mean (

\bar{x}

) of the dataset.

\bar{x} = \frac{3 + 7 + 8 + 10 + 12}{5} = \frac{40}{5} = 8

The mean is required to find individual deviations.

Compute the deviation of each observation from the mean,

(x - \bar{x})

3 - 8 = -5

7 - 8 = -1

8 - 8 = 0

10 - 8 = 2

12 - 8 = 4

Deviations quantify how far each data point lies from the central mean.

Square each deviation,

(x - \bar{x})^2

(-5)^2 = 25

(-1)^2 = 1

0^2 = 0

2^2 = 4

4^2 = 16

Squaring eliminates negative signs and weights larger deviations.

Sum the squared deviations and divide by the total number of observations

N = 5

Variance

\sigma^2 = \frac{25 + 1 + 0 + 4 + 16}{5} = \frac{46}{5} = 9.2

Variance is defined as the mean of the squared deviations.

Anahtar Kavram

Variance of Ungrouped Data

Tahmini Süre:1m 30s

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