Topic 1 Descriptive Statistics

Question 1

Data are time-consuming, ____, and of varying quality.

Answer 1

commercially sensitive

Question 2

A data set of size __ is denoted as: {xi}ᵢ₌₁,…,ₙ

Answer 2

n

Question 3

What’s the difference between a dot plot and a histogram?

Answer 3

Dot plots show individual data points (multi-frequency data set) while histograms group data into bins and show frequencies.

Question 4

What affects the appearance of a histogram the most?
A. Sample size
B. Axis label
C. Bin size
D. Title

Answer 4

C. Bin size

Question 5

Relative frequency = frequency / ____

Answer 5

total number of data points (n)

Question 6

What is plotted on the vertical axis of a histogram?

Answer 6

The absolute (or relative) frequency is plotted on the
vertical axis

Question 7

What does F(x) in a CDF plot represent?

Answer 7

The relative frequency of data ≤ x

Question 8

What is the downside of using histograms?

Answer 8

Downside is that histogram differs depending on bin size

Question 9

F(x) =

Answer 9

• 0 if x < x₍₁₎
• j/n if xⱼ ≤ x < xⱼ₊₁
• 1 if x ≥ x₍ₙ₎

Question 10

Formula for Arithmetic Mean

Answer 10

x̄ = (1/n) ∑xi

Question 11

Which measure is affected most by outliers?

Answer 11

Mean

Question 12

Which is not a measure of central tendency?
A. Median
B. Mode
C. Range
D. Mean

Answer 12

C. Range

Question 13

The geometric mean is only used for ____ data.

Answer 13

non-zero

Question 14

What does interquartile range (IQR) measure?

Answer 14

The spread between Q3 and Q1 (middle 50% of data)

Question 15

Formula for Sample variance (unbiased)

Answer 15

s² = (1/(n−1)) ∑(xi − x̄)²

Question 16

Formula for Sample Standard Deviation (unbiased)

Answer 16

s = √(s²) = √[(1/(n−1)) ∑(xi − x̄)²]

Question 17

What measures asymmetry?

Answer 17

Skewness

Question 18

The coefficient of variation is given by: vx = ____ / x̄

Answer 18

standard deviation (sx)

Question 19

Why is the mean absolute deviation more robust than standard deviation?

Answer 19

It is less influenced by outliers

Question 20

What does a positive skew indicate about the data?

Answer 20

Mean > Median > Mode

Question 21

Formula
Biased skewness:

Answer 21

g₁(x) = (1/n) ∑(xi − x̄)³ / ωₓ³

Question 22

Skewness is a ____ quantity (unit-less).

Answer 22

non-dimensional

Question 23

What is the median if n is odd?

Answer 23

median(x) = x₍ₙ₊½₎

Question 24

What is the mode?

Answer 24

The most common value

Question 25

Formula for geometric mean:

Answer 25

x* = (∏ⁿᵢ₌₁ xᵢ)¹⁄ⁿ

Question 26

What is used to test if two datasets have a linear relationship?

Answer 26

Covariance and correlation coefficient

Question 27

Formula Sample covariance:

Answer 27

cov(x,y) = (1/(n−1)) ∑(xi − x̄)(yi − ȳ)

Question 28

Formula Correlation coefficient:

Answer 28

cₓᵧ = (1/(n−1)) ∑(xi − x̄)(yi − ȳ) / (sx·sy)

Question 29

A correlation coefficient of 0 means ____ correlation.

Answer 29

no

Question 30

What is the range of correlation coefficient cₓᵧ? A. [−2, 2] B. [0, 1] C. [−1, 1] D. [−∞, ∞]

Answer 30

C. [−1, 1]

Question 31

What does a negative skew indicate about the data?

Answer 31

mode > median > mean

Question 32

What does a symmetric skew indicate about the data?

Answer 32

mode= median= mean

Question 33

The quantile value for the i-th data point is given by:

Answer 33

yᵢ = (i − 0.5)/n

Question 34

To determine the percentile qₚ(x), which condition must j satisfy? A. j < p B. j − 0.5/n < p/100 ≤ j + 0.5/n C. j/n > p D. j = p + 0.5

Answer 34

B. j − 0.5/n < p/100 ≤ j + 0.5/n

Question 35

To estimate qₚ(x), take the mean of data values at positions xⱼ and ____.

Answer 35

xⱼ₊₁