The heights (in cm) of a seedling recorded over five consecutive weeks are 9, 13, 15, 17, … — JAMB UTME

The heights (in cm) of a seedling recorded over five consecutive weeks are $9$ , $13$ , $15$ , $17$ , and $21$ . What is the standard deviation of the heights?

Answer: 4 cm

Answer

The standard deviation of the seedling heights is 4 cm.

To find the standard deviation, first compute the mean: (9 + 13 + 15 + 17 + 21) / 5 = 15. Next, calculate the sum of squared deviations: (-6)^2 + (-2)^2 + 0^2 + 2^2 + 6^2 = 36 + 4 + 0 + 4 + 36 = 80. Divide by 5 to find the variance of 16. Finally, taking the square root of 16 gives the standard deviation of 4 cm.

Step-by-Step Solution

Calculate the mean of the data values

Mean = 15 cm

The mean is necessary to calculate the deviations of each data point.

Calculate the squared deviations from the mean

Squared deviations are 36, 4, 0, 4, and 36 (sum = 80)

Variance measures the average of squared deviations from the mean.

Calculate the population variance

Variance = 80 / 5 = 16

Dividing the sum of squared deviations by N gives the variance.

Calculate the standard deviation

Standard deviation = sqrt(16) = 4 cm

The standard deviation is the square root of the variance.

Key Concept

Standard Deviation of Ungrouped Data

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