Ch.3 Numeric Descriptive Measures

Question 1

μ vs x-bar

Answer 1

Mean of
Population vs Sample

μ =∑x / N

Question 2

Positively Skewed
if Mean __ Median

Answer 2

Mean > Median

Question 3

Symmetrical
if Mean __ Median

Answer 3

Mean = Median = Mode

Question 4

σ²

Answer 4

Variance 方差 (sigma²)

σ² = ∑(x-μ)² / N

Measure of Spread = Avg Distance² from Mean

Question 5

σ

Answer 5

Standard Deviation (sigma)

Distance from Mean on avg

Question 6

Chebyshev’s Theorem:
Empirical Rule

when:
μ ± 1σ
μ ± 2σ
μ ± 3σ

Answer 6

≈68%
≈95%
≈99.7%

(μ@middle)

Question 7

In Box Plot
Q₁=
Q₂=
Q₃=
IQR=
(Interquartile Range)
Lower Limit=
Upper Limit=
Range=
& Outlier

Answer 7

Q₁= 25%
Q₂= 50% Median
Q₃= 75%
QUARTILE.EXC
IQR= Q₃ - Q₁
Lower Limit= Q₁- 1.5IQR
Upper Limit= Q₃+1.5IQR
Range= Max-Min
Outlier :
> Upper Limit or
< Lower Limit

Question 8

Frequency Table
(f & x):

Mean
Median
Mode

Answer 8

Mean= ∑fx / ∑f
Median= the Class (x) of [(∑f)+1]/2 locates
Mode= the Class (x) of most x’s

Question 9

Frequency Table
(f & x):

s² Variance=

Answer 9

Variance
∑f·(x-xbar)²
s² = —————
n-1

Question 10

s² Variance

(no frequency)

Answer 10

Variance
∑(x-xbar)²
s² = —————
n-1

Question 11

Coefficient of Variance

CV =
population & sample

Answer 11

CV= σ / μ (%)
population

CV= s / xbar (%)
sample

CV ↑ ⇒ Variable ↑

Question 12

Frequency Distribution Table
w/ Classes

e.g. 15 to under 30

Answer 12

Find Mid Point as x

e.g. 22.5 = (15+30)/2

Question 13

Chebyshev’s Theorem:
Non-Normal Proportion Data Set
How to find k in
μ ± kσ or
xbar ± ks

Answer 13

% ≥ 1- 1/k²