Dataset X consists of 2 numbers, each equal to 10. Dataset Y consists of 8 numbers, each e… — GRE General Test

Dataset $X$ consists of 2 numbers, each equal to 10. Dataset $Y$ consists of 8 numbers, each equal to 25. If Dataset $X$ and Dataset $Y$ are combined to form a single dataset of 10 numbers, what is the standard deviation of the combined dataset?

Answer: 6

Answer

The standard deviation of the combined dataset is 6.

To find the standard deviation of the combined dataset, first calculate the combined mean:

\frac{2(10) + 8(25)}{10} = 22

. Next, compute the variance by finding the average of the squared deviations from 22:

\frac{2(10 - 22)^2 + 8(25 - 22)^2}{10} = \frac{2(144) + 8(9)}{10} = \frac{360}{10} = 36

. Taking the square root of the variance yields a standard deviation of

\sqrt{36} = 6

Step-by-Step Solution

Calculate the mean of the combined 10-number dataset.

The combined mean is 22.

The mean of the combined dataset is needed to compute individual deviations.

Compute the squared deviation of each data point from the combined mean and average them to determine the variance.

The variance is 36.

Variance is defined as the arithmetic mean of the squared deviations from the mean.

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

The standard deviation is 6.

Standard deviation is the non-negative square root of variance.

Key Concept

Standard deviation of a combined dataset

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