A sample of 12 measurements has a mean of 34 and a standard deviation of 4.5. Suppose that the sample is enlarged to 14 measurements, by including two additional measurements having a common value of 34 each.

A. Find the mean of the sample of 14 measurements.

Mean =

B. Find the standard deviation of the sample of 14 measurements.

Standard Deviation =

Since the two additional scores = the mean, the mean and the standard deviation will not change.

WRONG!

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To find the mean of the sample of 14 measurements, you need to add up all the measurements and divide by the total number of measurements.

A. Find the mean of the sample of 14 measurements:

First, calculate the sum of the original 12 measurements:
Sum = 12 * Mean = 12 * 34 = 408

Then, add the values of the two additional measurements:
Sum += 2 * 34 = 408 + 68 = 476

Now, divide the sum by the total number of measurements (14 in this case) to find the mean:
Mean = Sum / Total number of measurements = 476 / 14 = 34

Therefore, the mean of the sample of 14 measurements is 34.

To find the standard deviation of the sample of 14 measurements, you need to use the formula for the standard deviation.

B. Find the standard deviation of the sample of 14 measurements:

The formula for the standard deviation is given by:

Standard Deviation = √( Σ(x - x̄)² / N )

Where Σ denotes the sum of the squared differences from the mean, x is each individual measurement, x̄ is the mean of the sample, and N is the total number of measurements.

Let's break down the calculation:

1. Calculate the squared differences from the mean for each measurement, including the two additional measurements:
(34 - 34)² + (34 - 34)² + ... + (34 - 34)² (12 times)
= 0 + 0 + ... + 0 (12 times)
= 0

2. Add the squared differences:
Σ(x - x̄)² = 0

3. Divide the sum by the total number of measurements (14) to find the variance:
Variance = Σ(x - x̄)² / N = 0 / 14 = 0

4. Finally, take the square root of the variance to find the standard deviation:
Standard Deviation = √(Variance) = √(0) = 0

Therefore, the standard deviation of the sample of 14 measurements is 0.