A library recorded the number of books borrowed over five consecutive days as 2, 4, 5, 6, … — JAMB UTME

A library recorded the number of books borrowed over five consecutive days as $2$ , $4$ , $5$ , $6$ , and $8$ . What is the standard deviation of the number of books borrowed?

$2$ Cevap
B
$4$
C
$5$
D
$6$

Cevap

The standard deviation of the number of books borrowed is

2

The mean of the five data points is

5

. The sum of the squared deviations from the mean is

9 + 1 + 0 + 1 + 9 = 20

. Dividing by

5

gives a variance of

4

. Taking the square root of

4

yields the standard deviation of

2

Adım Adım Çözüm

Calculate the arithmetic mean (

\bar{x}

) of the given dataset.

\bar{x} = \frac{2 + 4 + 5 + 6 + 8}{5} = \frac{25}{5} = 5

The mean is required to determine the deviations of each data point.

Find the deviations from the mean

(x - \bar{x})

and square each deviation

(x - \bar{x})^2

(2-5)^2 = 9, \quad (4-5)^2 = 1, \quad (5-5)^2 = 0, \quad (6-5)^2 = 1, \quad (8-5)^2 = 9

Squaring ensures all deviation values are positive before summation.

Calculate the variance (mean of squared deviations).

\text{Variance } (\sigma^2) = \frac{9 + 1 + 0 + 1 + 9}{5} = \frac{20}{5} = 4

Variance measures the average squared spread around the mean.

Take the square root of the variance to find the standard deviation.

\text{Standard Deviation } (\sigma) = \sqrt{4} = 2

Standard deviation expresses dispersion in the original unit of measurement.

Anahtar Kavram

Standard Deviation of Ungrouped Data

Soru

Cevap

Adım Adım Çözüm

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