Question

identify the symbols used for each of the following: (a) sample standard deviation; (b) population standard deviation; (c) sample variance; (d) population variance. if sample data consist of weights measured in grams, what units are used for these statistics and parameters?
a. the symbol for sample standard deviation is s.
b. the symbol for population standard deviation is σ.
c. the symbol for sample variance is s².
d. the symbol for population variance is σ².
if sample data consist of weights measured in grams, then correctly complete the following sentences.
a. the unit for sample standard deviation would be dropdown
b. the unit for population standard deviation would be dropdown
c. the unit for sample variance would be dropdown
d. the unit for population variance would be dropdown
the dropdown options include g, g², g³, √g.

Explanation:

Part 1: Identifying Symbols

a. Sample Standard Deviation

The symbol for sample standard deviation is \( s \). This is a well - known statistic notation where \( s \) is used to represent the standard deviation calculated from a sample of data.

b. Population Standard Deviation

The symbol for population standard deviation is \( \sigma \). In statistics, \( \sigma \) is the Greek letter used to denote the standard deviation of an entire population.

c. Sample Variance

The symbol for sample variance is \( s^{2} \). Variance is the square of the standard deviation, and for a sample, we use \( s \) for standard deviation, so the variance (which is the square of the standard deviation) is \( s^{2} \).

d. Population Variance

The symbol for population variance is \( \sigma^{2} \). Since the population standard deviation is \( \sigma \), the population variance (the square of the population standard deviation) is \( \sigma^{2} \).

Part 2: Determining Units

The original data (weights) is measured in grams.

a. Sample Standard Deviation

The unit of sample standard deviation will be the same as the unit of the original data. So if the original data is in grams, the unit for sample standard deviation (\( s \)) is grams (g).

b. Population Standard Deviation

Similar to the sample standard deviation, the population standard deviation (\( \sigma \)) also has the same unit as the original data. So the unit for population standard deviation is grams (g).

c. Sample Variance

Variance is the square of the standard deviation. If the standard deviation has a unit of grams (g), then the variance (which is the square of the standard deviation) will have a unit of \( \text{grams}^2 \) (or \( g^{2} \)). So the unit for sample variance (\( s^{2} \)) is \( g^{2} \).

d. Population Variance

The population variance (\( \sigma^{2} \)) is the square of the population standard deviation. Since the population standard deviation has a unit of grams (g), the population variance will have a unit of \( \text{grams}^2 \) (or \( g^{2} \)).

Final Answers

Symbols:

a. \( s \)
b. \( \sigma \)
c. \( s^{2} \)
d. \( \sigma^{2} \)

Units (when data is in grams):

a. \( g \)
b. \( g \)
c. \( g^{2} \)
d. \( g^{2} \)

Answer:

Part 1: Identifying Symbols

a. Sample Standard Deviation

The symbol for sample standard deviation is \( s \). This is a well - known statistic notation where \( s \) is used to represent the standard deviation calculated from a sample of data.

b. Population Standard Deviation

The symbol for population standard deviation is \( \sigma \). In statistics, \( \sigma \) is the Greek letter used to denote the standard deviation of an entire population.

c. Sample Variance

The symbol for sample variance is \( s^{2} \). Variance is the square of the standard deviation, and for a sample, we use \( s \) for standard deviation, so the variance (which is the square of the standard deviation) is \( s^{2} \).

d. Population Variance

The symbol for population variance is \( \sigma^{2} \). Since the population standard deviation is \( \sigma \), the population variance (the square of the population standard deviation) is \( \sigma^{2} \).

Part 2: Determining Units

The original data (weights) is measured in grams.

a. Sample Standard Deviation

The unit of sample standard deviation will be the same as the unit of the original data. So if the original data is in grams, the unit for sample standard deviation (\( s \)) is grams (g).

b. Population Standard Deviation

Similar to the sample standard deviation, the population standard deviation (\( \sigma \)) also has the same unit as the original data. So the unit for population standard deviation is grams (g).

c. Sample Variance

Variance is the square of the standard deviation. If the standard deviation has a unit of grams (g), then the variance (which is the square of the standard deviation) will have a unit of \( \text{grams}^2 \) (or \( g^{2} \)). So the unit for sample variance (\( s^{2} \)) is \( g^{2} \).

d. Population Variance

The population variance (\( \sigma^{2} \)) is the square of the population standard deviation. Since the population standard deviation has a unit of grams (g), the population variance will have a unit of \( \text{grams}^2 \) (or \( g^{2} \)).

Final Answers

Symbols:

a. \( s \)
b. \( \sigma \)
c. \( s^{2} \)
d. \( \sigma^{2} \)

Units (when data is in grams):

a. \( g \)
b. \( g \)
c. \( g^{2} \)
d. \( g^{2} \)