Chapter 3: Descriptive Statistics

Question 1

Descriptive Statistics

Answer 1

graphical + numerical methods of summarizing data

Question 2

Inferental statistics

Answer 2

uses descriptive statistics to estimate and make inferences about population parameters

Question 3

Summation, Σ

Answer 3

means “add up everything that follows”

Question 4

PEMDAS (order of operations)

Answer 4

1. Parentheses
2. Exponents
3. Multiplication/division
4. Addition/subtraction
5. Summation

Question 5

Mean

Answer 5

arithmetic average of the numbers

Question 6

Statistic

Answer 6

any characteristic or measure from a SAMPLE

Question 7

Parameter

Answer 7

any characteristic or measure from a POPULATION

Question 8

Median

Answer 8

data value in the middle of the ordered data

Question 9

Mode

Answer 9

the data value that occurs most frequently in the data

Question 10

Outlier

Answer 10

data value that is very different from the rest of the data and is far from the median

Question 11

Variability

Answer 11

describes how the data is spread out

Question 12

High variability indicates what about the data?

Answer 12

Data is spread out

Question 13

Low variability indicates what about the data?

Answer 13

Data is close together

Question 14

Range

Answer 14

difference between highest and lowest data values

Question 15

Deviation

Answer 15

how far each data point is from the mean (𝑥 − 𝑥̅)

Question 16

Variance

Answer 16

measure of the average squared distance from the mean

Question 17

Standard deviation

Answer 17

Average (mean) distance from a data point to the mean; how much a typical data point differs from the mean

Question 18

What is inferred by a small standard deviation?

Answer 18

Data is close together

Question 19

What is inferred by a large standard deviation?

Answer 19

Data is spread out

Question 20

When should you compare the range, standard deviation, or variance values of different sets of data?

Answer 20

ONLY when the two data sets have the same units/scales

Question 21

Coefficient of variation (CVar)

Answer 21

standard deviation divided by mean, expressed as percentage

Question 22

Find the coefficient of variation for a Crumbl cookie, when the average price is 𝑥̅ = $4.50, and standard deviation is s = $0.36. Round to two decimal places

Answer 22

CVar = (s/𝑥̅)x100% = 8.00%

Question 23

Z-score

Answer 23

number of standard deviations an observation (x value) is above or below the mean
-if z-score is +1.00, the x-value is 1 standard deviation above the mean
-if z-score is -3.50, the x-value is 3.5 standard deviations below the mean

Question 24

What two things does a z-score always have?

Answer 24

-a sign; + or -, and
-two decimal places

Question 25

Independent variable (x)

Answer 25

explains causes/changed in dependent variable; the MANIPULATED variable

Question 26

Dependent variable (y)

Answer 26

measures the outcome of the study; the MEASURED variable

Question 27

Correlation (r)

Answer 27

a way to see if two quantitative variables are related/connected -values range from -1.00 to +1.00

Question 28

True or False: correlation implies causation

Answer 28

False

Question 29

Positive r indicates:

Answer 29

positive correlation; as x increases, y increases

Question 30

Negative r indicates:

Answer 30

negative correlation; as x increases, y decreases

Question 31

r = 0.00 means that:

Answer 31

there is a weak linear relationship between x and y

Question 32

What is the range of this set of data values? 15, 18, 11, 20, 17

Answer 32

range = [max - min] = 9

Question 33

What is the sample mean of this set of data values? Round to two decimal places. 15, 18, 11, 20, 17

Answer 33

sample mean = (Σx)/n 16.20

Question 34

What is the summation of all deviation scores of this set of data values? 15, 18, 11, 20, 17

Answer 34

Σ(x-𝑥̅ ) = 0

Question 35

What is the summation of the squared deviation of this set of data values? Round to two decimal places. 15, 18, 11, 20, 17

Answer 35

Σ(x-𝑥̅ )^2 = 46.80

Question 36

What is the sample variance from this set of data values? Round to two decimal places. 15, 18, 11, 20, 17

Answer 36

[Σ(x-𝑥̅ )^2]/n-1 = 46.8/4 =11.70 units ^2

Question 37

What is the standard deviation for this set of data values? Round to two decimal places. 15, 18, 11, 20, 17

Answer 37

√[Σ(x-𝑥̅ )^2]/n-1 = 3.42 units

Question 38

What is the coefficient of variation of this set of data values? Round to two decimal places. 15, 18, 11, 20, 17

Answer 38

CVar= (s/v)x100% = (3.4/16.2)x100% = 20.98%