8 Common Techniques in Descriptive Statistics

Question 1

What are the main topics covered in this chapter?

Answer 1

• Understanding frequencies and percentages
• Calculating percent change and percent difference
• Discovering confidence intervals
• Understanding z-scores

Question 2

Define frequencies in the context of descriptive statistics.

Answer 2

A count of occurrences of specific values within a variable.

Question 3

What is a frequency table?

Answer 3

A table that lists every reported value in a variable and how many times they occurred.

Question 4

What is the purpose of a contingency table?

Answer 4

To hold more than one variable and show the relationship between them.

Question 5

How do you calculate frequency?

Answer 5

1. Arrange values in order.
2. Create a table of possible values.
3. Count occurrences of each value.

Question 6

What is the difference between count and probability in statistics?

Answer 6

Count is the number of occurrences, while probability is the count divided by the total number of occurrences.

Question 7

What are percentages in relation to frequencies?

Answer 7

Percentages represent the portion of the whole that each value accounts for.

Question 8

List the steps to calculate percentages.

Answer 8

1. Find the frequencies.
2. Divide each frequency by the total number of values.
3. Multiply each frequency by 100.

Question 9

Fill in the blank: Percent change is concerned with how a single value has changed from point A to point _______.

Answer 9

[B]

Question 10

What is the formula for calculating percent change?

Answer 10

C = ((x2 - x1) / x1) * 100

Question 11

True or False: Percent change can yield negative results.

Answer 11

True

Question 12

What is the main focus of percent difference?

Answer 12

Comparing two values without a designated starting point.

Question 13

What is the formula for calculating percent difference?

Answer 13

Percent difference = (|x1 - x2| / ((x1 + x2) / 2)) * 100

Question 14

Fill in the blank: Percent difference will never have a _______ value.

Answer 14

[negative]

Question 15

What type of data do frequencies and percentages commonly apply to?

Answer 15

Qualitative variables

Question 16

What happens to the complexity of frequency tables as more variables are added?

Answer 16

Complexity increases exponentially.

Question 17

What type of chart represents frequencies?

Answer 17

Bar charts

Question 18

What type of chart represents percentages?

Answer 18

Pie charts

Question 19

True or False: Percent change and percent difference are calculated the same way.

Answer 19

False

Question 20

What is the key difference between percent change and percent difference?

Answer 20

Percent change references a starting value; percent difference treats both values equally.

Question 21

How would you describe the relationship between percent change and a variable’s starting point?

Answer 21

Percent change is always reported in reference to a starting value.

Question 22

What is the significance of understanding confidence intervals in data analysis?

Question 23

What is a z-score used for in statistics?

Question 24

What is the formula for calculating percent difference?

Answer 24

Percent difference = (|𝑥𝑥1 - 𝑥𝑥2| / ((𝑥𝑥1 + 𝑥𝑥2) / 2)) * 100

Question 25

What is the first step in calculating percent difference?

Answer 25

Subtract one value from the other and drop any negative signs.

Question 26

True or False: Percent difference can have negative values.

Answer 26

False

Question 27

What does a confidence interval represent?

Answer 27

A range including the mean of your sample.

Question 28

What is the most common alpha value used for confidence intervals?

Answer 28

0.05

Question 29

What confidence level corresponds to an alpha of 0.05?

Answer 29

95%

Question 30

What is the equation for calculating a confidence interval?

Answer 30

CI = 𝑥𝑥̅ ± t (𝜎 / √𝑛)

Question 31

What does 𝑥𝑥̅ represent in the confidence interval equation?

Answer 31

The mean of the sample.

Question 32

What is the purpose of a z-score?

Answer 32

To compare a single value to a normal distribution.

Question 33

Fill in the blank: A z-score reports how many _______ your chosen value is from the mean.

Answer 33

standard deviations

Question 34

What is the equation for calculating a z-score?

Answer 34

Z = (𝑥𝑥 - 𝜇𝜇) / 𝜎𝜎

Question 35

What is the first step in calculating a z-score?

Answer 35

Subtract the mean from your value.

Question 36

How do you find the upper confidence interval?

Answer 36

Add the result of the previous step to your mean.

Question 37

How do you find the lower confidence interval?

Answer 37

Subtract the result of the previous step from the mean.

Question 38

What does 't' represent in the confidence interval equation?

Answer 38

A value from a t-distribution confidence table.

Question 39

What is the standard deviation of the sample in the hotdog sales example?

Answer 39

1.12

Question 40

What is the sample size in the hotdog sales example?

Answer 40

9

Question 41

What is the mean of the hotdog sales example?

Answer 41

8

Question 42

What is the result of the confidence interval calculation for the hotdog sales?

Answer 42

Lower confidence interval = 7.31, Upper confidence interval = 8.69

Question 43

What type of analysis is most appropriate for comparing a single article's reads to other articles?

Answer 43

Z-score

Question 44

What is the confidence level if the alpha is 0.01?

Answer 44

99%

Question 45

True or False: The percent change measures the objective difference between two values.

Answer 45

False

Question 46

What do you need to calculate percent change?

Answer 46

A starting value and an ending value.

Question 47

What is the percent change if the starting value is 200 and the ending value is 240?

Answer 47

20%

Question 48

What is the second step in calculating percent difference?

Answer 48

Find the average of the two values.

Question 49

What is the third step in calculating confidence intervals?

Answer 49

Find the square root of your sample size.

Question 50

What is the significance of the degrees of freedom (dfs) in the context of confidence intervals?

Answer 50

Sample size minus 1.

Question 51

What does a z-score of 1 indicate in terms of standard deviation?

Answer 51

The value is 1 standard deviation above the mean.