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The table shows the means and ranges of two data sets, X and Y, each containing the same number of measurements.

Quantity A

The standard deviation of data set X

Quantity B

The standard deviation of data set Y
The standard deviation of n numbers $$x_{1}$$, $$x_{2}$$, $$x_{3}$$,......, $$x_{n}$$, with mean $$\overline{x}$$ is equal to $$\sqrt{\frac{s}{n}}$$, where S is the sum of the squared differences $$(x_{i} - \overline{x})^{2}$$ for 1 ≤ i ≤ n.

If the standard deviation of the 5 numbers 20-2c, 20-c, 20, 20+c, and 20+2c is greater than 6, which of the following could be the value of c?

Indicate all such values.
The standard deviation of n numbers $$x_{1}$$, $$x_{2}$$, $$x_{3}$$,......, $$x_{n}$$, with mean x is equal to $$\sqrt{\frac{s}{n}}$$, where S is the sum of the squared differences, $$(x_{i} - x)^{2}$$ for 1 ≤ i ≤ n.

In a set of data, 1 appears k times, 5 appears k times, and 3 appears once. What is the minimum k to make the standard deviation greater than 1.95 ?
The average of a list of 17 numbers is 0, and the standard deviation of these numbers is 40. If a new number is added to the list, the average remains the same, then what is the new standard deviation of the list?

Give your answer to the nearest hundredths digit.
Set A={1, 2, 3, 4, 5}

Set B={6, 7, 8, 9, 10}

Quantity A

The standard deviation of all the numbers in Set A

Quantity B

The standard deviation of all the numbers in Set B
List A: 13.2, 14.2, 15.2, 16.2, 17.2

List B can be formed by dividing all the numbers in List A by 0.2

List C can be formed by multiplying all the numbers in List A by 0.2

Which of the following statement illustrates the exact order of standard deviation of these lists of numbers from the lowest to the greatest?
List B is composed by subtracting 5 from each number in List A.

Which aspect of List B is 5 less than the same aspect of List A?

Indicate all such aspects.
In the xy-plane, 8 data points lie on the line with equation y=40+5x. If the standard deviation of the x-coordinates of the 8 points is 4.6, what is the standard deviation of the y-coordinates of the 8 points?
List A: 27, 28, 30, 32, 33

List B: 28, 29, 30, 31, 32

List C: 37, 38, 40, 42, 43

List D: 38, 39, 40, 41, 42

Which of the following statements illustrate the exact order of standard deviation of these sets of numbers from the greatest to the lowest?

Quantity A

The standard deviation of the numbers 45, 64, 83, and 53

Quantity B

The standard deviation of the numbers 55, 81, 47, and 62
Set A={9, 13, 4, 2, 7}

Set B={9, 13, 4, 2, 9}

Set C={9, 13, 4, 2, 4}

Set D={9, 13, 4, 2, 6}

Which of the following statement illustrates the exact order of standard deviation of these sets of numbers from the lowest to the greatest?
Five different families received tax bills at the beginning of the year. Later, the four lowest tax bills were each reduced by $200 while the highest tax bill remained the same.

Quantity A

The standard deviation of the original five tax bills

Quantity B

The standard deviation of the resulting five tax bills after the four lowest tax bills were reduced
As a part of an environmental study of a river, a random sample of trout was drawn from the river and the lengths of the trout were recorded. The average (arithmetic mean) length was 14.31 inches. If a length of 16.89 inches was 1.50 standard deviations above the average, what was the standard deviation of the lengths of the trout in the sample?
The standard deviation of numbers in List A is 6, while the standard deviation of numbers in List B is 8

Quantity A

2 standard deviation above the mean in list A

Quantity B

1 standard deviation above the mean in list B
In the distribution of the weights of the fish in a certain sample, a weight of 30 pounds is 2.2 standard deviations above the mean and a weight of 14 pounds is 1.8 standard deviations below the mean. What is the mean of the wveights of the fish in this sample, to the nearest pound?
For a certain normal distribution, the value 15.6 is 2 standard deviations below the mean of the distribution and the value 26.1 is 3 standard deviations above the mean of the distribution. What is the mean of the distribution?
In a list of numbers, 20.0 is 2 standard deviation above the mean, while 6.5 is 3 standard deviation below the mean.

Quantity A

The average of the list of numbers

Quantity B

14.6


The table above summarizes customer satisfaction ratings for two banks, where each rating is an integer from 1 to 10. Which of the following statements must be true?

Indicate all such statements.


The random variable X has the standard normal distribution with a mean of 0 and a standard deviation of 1, as shown. Probabilities, rounded to the nearest 0.01, are indicated for the six intervals shown. The random variable Y has a normal distribution with a mean of 2 and a standard deviation of 1. Using the probabilities shown, approximately how much greater is the probability that the value of Y is between 1 and 2 than the probability that the value of X is between 1 and 2?
In a normal distribution of data x, the mean is 400, while the standard deviation is 60.

Quantity A

P(400 < x < 430)

Quantity B

P(430 < x < 460)

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