Lesson 5 formulas

Question 1

Mean Absolute Deviation (MAD)

Answer 1

is the average of the summation of the absolute deviation of each observation from the mean

MAD = ∑|X – x̄ | / N

Question 2

Ungrouped Data

Variance

Answer 2

is the average of the squares of the differences between the individual (observed) and the expected value

PV
σ ² = ∑( X – x̄ ) ² / N

SV
s ² = ∑( X – x̄ ) ² / N - 1

where: 
X = value from raw data
x̄  = mean
N = total population

Question 3

Ungrouped Data

Standard deviation

Answer 3

is the square root of the average deviation from the mean, or simply the square root of the variance.

PSD
σ = √ ∑( X – x̄ ) ² / N

SSD
s = √ ∑( X – x̄ ) ² / N - 1

where: 
X = value from raw data
x̄  = mean
N = total population

Question 4

Coefficient of variation (cv)

Answer 4

is the ratio of the standard deviation to the mean

It is used to compare the variability of two or more sets of data even when they are expressed in different units of measurement.

cv = SD / x̄

where: 
cv = coefficient of variation
SD = standard deviation
x̄ = mean

Question 5

Grouped Data

Variance

Answer 5

is the average of the squares of the differences between the individual (observed) and the expected value

PV
σ ² = ∑f( X – x̄ ) ² / N

SV
s ² = ∑f( X – x̄ ) ² / N - 1

where: 
X = classmark
x̄  = mean
N = total population
f = frequency

Question 6

Grouped data

Standard deviation

Answer 6

is the square root of the average deviation from the mean, or simply the square root of the variance.

PSD
σ = √ ∑f( X – x̄ ) ² / N

SSD
s = √ ∑f( X – x̄ ) ² / N - 1

where: 
X = classmark
x̄  = mean
N = total population
f = frequency

Question 7

is the average of the summation of the absolute deviation of each observation from the mean

Answer 7

Mean Absolute Deviation (MAD)

MAD = ∑|X – x̄ | / N

Question 8

is the average of the squares of the differences between the individual (observed) and the expected value

Answer 8

Variance

Grouped data:

PV
σ ² = ∑f( X – x̄  ) ² / N

SV
s ² =   ∑f( X – x̄  ) ² / N - 1

Ungrouped data:

PV
σ ² = ∑( X – x̄  ) ² / N

SV
s ² =   ∑( X – x̄  ) ² / N - 1

Question 9

is the square root of the average deviation from the mean, or simply the square root of the variance.

Answer 9

Standard deviation

Grouped data:

PSD
σ =  √ ∑f( X – x̄  ) ² / N

SSD
s =  √ ∑f( X – x̄  ) ² / N - 1

Ungrouped data:

PSD
σ =  √ ∑( X – x̄  ) ² / N

SSD
s =  √ ∑( X – x̄  ) ² / N - 1

Question 10

is the ratio of the standard deviation to the mean

It is used to compare the variability of two or more sets of data even when they are expressed in different units of measurement.

Answer 10

Coefficient of variation (cv)

cv = SD / x̄

Question 11

Range (R)

Answer 11

is the difference between the highest and the lowest values

This is the simplest but the most unreliable measure of variability since it uses only two values in the distribution

R = Hv – Lv

where: R = Range
Hv = Highest Value
Lv = Lowest Value

Question 12

is the difference between the highest and the lowest values

This is the simplest but the most unreliable measure of variability since it uses only two values in the distribution

Answer 12

Range (R)

R = Hv – Lv

where: R = Range
Hv = Highest Value
Lv = Lowest Value

Question 13

coefficient of skewness

Answer 13

SK = 3(Mean – Median) / standard deviation

where: SK is the coefficient of skewness

Question 14

refers to the peakedness or flatness of a distribution

Answer 14

Kurtosis (ku)

Grouped data:

Ku = ∑ f(Xm – x̄ )⁴ / Ns ⁴

Ungrouped data:

Ku = ∑ (X – x̄  )⁴ / Ns ⁴

Where: Ku = kurtosis
X = raw score
Xm = class mark
X = mean
s⁴ = square of the variance
N = samples size