A research team measured the height, in centimeters, of 15 plants in a greenhouse. The dat… — GRE General Test

A research team measured the height, in centimeters, of 15 plants in a greenhouse. The dataset has a range of $24\text{ cm}$ , an interquartile range (IQR) of $10\text{ cm}$ , and a standard deviation of $5.2\text{ cm}$ . If the height of every plant is increased by exactly $8\text{ cm}$ , which of the following statements regarding the modified dataset must be true? Select all such statements.

A
The range of the modified dataset is $32\text{ cm}$ .
The range of the modified dataset is $24\text{ cm}$ .Cevap
C
The interquartile range of the modified dataset is $18\text{ cm}$ .
The standard deviation of the modified dataset is $5.2\text{ cm}$ .Cevap
E
The standard deviation of the modified dataset is $13.2\text{ cm}$ .

Cevap

The statement that the range of the modified dataset is

24\text{ cm}

and the statement that the standard deviation of the modified dataset is

5.2\text{ cm}

are both true.

When a constant is added to every value in a dataset, the entire distribution shifts by that amount. Consequently, the relative positions and distances between data points do not change, leaving measures of dispersion (range, IQR, standard deviation) unchanged. Therefore, the range remains

24\text{ cm}

and the standard deviation remains

5.2\text{ cm}

Adım Adım Çözüm

Analyze the effect of adding a constant to a dataset on measures of dispersion.

Adding a constant

k

to every data value shifts the center (mean, median) by

k

, but all measures of spread (range, IQR, standard deviation) remain completely unchanged.

Measures of dispersion quantify the spread or distance between data values, which is invariant under a uniform translation.

Evaluate each statement against the unchanged measures of dispersion.

The range remains

24\text{ cm}

, the IQR remains

10\text{ cm}

, and the standard deviation remains

5.2\text{ cm}

Comparing the calculated original measures to the statements shows that the range of

24\text{ cm}

and standard deviation of

5.2\text{ cm}

are correct.

Anahtar Kavram

Effect of Linear Transformations (Addition of a Constant) on Measures of Dispersion

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Konular

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