Class 6 Spring 🌷

Question 1

What are the two types of data that can be analyzed after sampling from a larger population?

Answer 1

Categorical and numerical data

Question 2

What are some ways to visualize data trends and distribution shape?

Answer 2

Table or graph (e.g., frequency plot, bar chart, histogram, box-and-whisker, scatterplot)

Question 3

What summary statistics are commonly calculated?

Answer 3

• Central tendency (mean, median, mode)
• Dispersion (range, IQR, standard deviation)

Question 4

What is the relationship between the type of table or graph and the nature of the variables?

Answer 4

It depends primarily on whether the variables are numerical or categorical

Question 5

What shape does a normal (Gaussian) distribution always have?

Answer 5

Bell-shaped and symmetrical around a central mean

Question 6

What does the area under the normal distribution curve always equal?

Answer 6

1

Question 7

What does the 68-95-99.7 Rule (Empirical Rule) describe?

Answer 7

• About 68% falls within 1 SD of the mean
• About 95% falls within 2 SD of the mean
• About 99.7% falls within 3 SD of the mean

Question 8

What is the formula for calculating a z-score?

Answer 8

(observation – population mean) / standard deviation

Question 9

What is the standard normal distribution notation?

Answer 9

N(µ = __, σ = __)

Question 10

How can z-scores be used in relation to different distributions?

Answer 10

To compare how unusual two measurements are, even when looking at different normal distributions

Question 11

What does a z-score represent?

Answer 11

The number of standard deviations an observation is above or below the mean

Question 12

True or False: Z-scores can be used for distributions of any shape.

Answer 12

False

Question 13

What is the probability that a randomly sampled US adult is between 180 cm and 185 cm estimated by?

Answer 13

The shaded area under the curve

Question 14

What statistical function in R is used to calculate the lower tail area based on a z-score?

Answer 14

pnorm()

Question 15

Fill in the blank: The area under the normal curve always adds up to _______.

Answer 15

1

Question 16

What happens to real-world data distributions compared to the normal distribution?

Answer 16

They will never produce a perfect curve

Question 17

What does a z-score of more than 3 signify?

Answer 17

Very unusual observations

Question 18

What is the mean and standard deviation for SAT scores?

Answer 18

Mean = 1500, Standard Deviation = 300

Question 19

What is the mean and standard deviation for ACT scores?

Answer 19

Mean = 21, Standard Deviation = 5

Question 20

What is the role of parameters in the normal distribution?

Answer 20

Parameters (mean µ and standard deviation σ) describe the normal distribution perfectly

Question 21

What method is used to find the probability of a measurement falling above a particular cutoff value?

Answer 21

1 - pnorm(value)

Question 22

What is the probability that a random student scores at least 1190 on her SATs calculated using?

Answer 22

1 - pnorm(z-score)

Question 23

What is the mean height of male adults in the US?

Answer 23

70.0”

Question 24

What is the standard deviation of heights for male adults in the US?

Answer 24

3.3”

Question 25

What is the first use of z-scores?

Answer 25

To compare distributions by standardizing measurements/observations to z-scores

Question 26

What does the second use of z-scores allow you to calculate?

Answer 26

The percentile of a cutoff value

Question 27

What is the third use of z-scores?

Answer 27

To calculate the probability that a measurement will fall ABOVE a particular cutoff value

Question 28

What can you calculate using z-scores related to two values?

Answer 28

The probability that a measurement will fall BETWEEN two values

Question 29

What does the area below a cutoff value represent?

Answer 29

Area to the left

Question 30

How do you calculate the area above a cutoff value?

Answer 30

1 - pnorm()

Question 31

How is the area between two values calculated?

Answer 31

Area to left of higher value - area to left of lower value

Question 32

What does the 68-95-99.7 Rule describe?

Answer 32

Distribution of data in a normal distribution

Question 33

What percentage of data falls within 1 standard deviation of the mean according to the 68-95-99.7 Rule?

Answer 33

68%

Question 34

What percentage of data falls within 2 standard deviations of the mean according to the 68-95-99.7 Rule?

Answer 34

95%

Question 35

What percentage of data falls within 3 standard deviations of the mean according to the 68-95-99.7 Rule?

Answer 35

99.7%

Question 36

What is considered 'unusual' in terms of standard deviations from the mean?

Answer 36

> 2 SD

Question 37

What is considered 'very unusual' in terms of standard deviations from the mean?

Answer 37

> 3 SD

Question 38

What are the SAT score ranges for the 68-95-99.7 Rule?

Answer 38

* ~68%: between 1200 and 1800 * ~95%: between 900 and 2100 * ~99.7%: between 600 and 2400

Question 39

What function is used in R to find a z-score from an area?

Answer 39

qnorm

Question 40

Fill in the blank: To find the z-score for a data point that is bigger than 40% of other data points, you would use _______.

Answer 40

qnorm(0.4)

Question 41

How can you manually input mean and standard deviation in R?

Answer 41

Using qnorm(area, mean=mean_value, sd=sd_value)