STK – Chapter 3 Notes
When a data set contains more than one variable, the same numerical measures can
be computed separately for each variable.
Sample statistics = A numerical value used as a summary measure for a sample (e.g., the
sample mean, ẋ, the sample variance, s2, and the sample standard deviation, s).
If the measures are computed for data from a sample
Population parameters = A numerical value used as a summary measure for a population
(e.g., the population mean, μ , the population variance, σ 2 , and the population standard
deviation, σ ). If the measures are computed for data from a population.
Point estimator = aka, a sample statistic, such as, ẋ, s2, and s, used to estimate the
corresponding population parameter.
Section 3.1 measures of location
1. Mean = is sometimes referred to as the arithmetic mean/ average value, A measure of central
location computed by summing the data values and dividing by the number of observations.
Data for sample, mean is denoted by x bar
Data for population, mean is denoted by Greek letter μ
The value of variable x for the ith observation is denoted by xi. For a sample with n
observations, the formula for the sample mean is as follows.
The sample mean is a sample statistic
The E is the summation sign
n is the total
The sample mean is a point of estimator of the population mean
N is the no. of observations in a population
The μ is symbol for a population mean
, 2. Median = A measure of central location provided by the value in the middle when the data are
arranged in ascending order (smallest to largest).
- Odd numbers has a middle value
- Even numbers have a single middle value (x + x/2)
3. Mode = A measure of location, defined as the value that occurs with greatest frequency.
- Bimodal = if the data contains exactly two modes
- Multimodal = if data contains more than two modes
Excel Functions:
Mean = AVERAGE(B2:B13)
Median = MEDIAN(B2:B13)
Mode = MODE.SNGL(B2:B13)
4. Weighted Mean = the mean obtained by assigning each observation a weight that reflects its
importance.
Where wi is weight for observation i
When data is from sample: x bar
When data is from population: μ
5. Geometric Mean = A measure of location that is calculated by finding the nth root of the
product of n values. It is applied to find the mean rate of change over quarters, months, weeks,
and even days
Function: used to analyse growth rates in financial data (average mean in this case will be
misleading)
Excel function:
For growth rate =1+.01*B2
Geometric mean = GEOMEAN(C2:C11)
When a data set contains more than one variable, the same numerical measures can
be computed separately for each variable.
Sample statistics = A numerical value used as a summary measure for a sample (e.g., the
sample mean, ẋ, the sample variance, s2, and the sample standard deviation, s).
If the measures are computed for data from a sample
Population parameters = A numerical value used as a summary measure for a population
(e.g., the population mean, μ , the population variance, σ 2 , and the population standard
deviation, σ ). If the measures are computed for data from a population.
Point estimator = aka, a sample statistic, such as, ẋ, s2, and s, used to estimate the
corresponding population parameter.
Section 3.1 measures of location
1. Mean = is sometimes referred to as the arithmetic mean/ average value, A measure of central
location computed by summing the data values and dividing by the number of observations.
Data for sample, mean is denoted by x bar
Data for population, mean is denoted by Greek letter μ
The value of variable x for the ith observation is denoted by xi. For a sample with n
observations, the formula for the sample mean is as follows.
The sample mean is a sample statistic
The E is the summation sign
n is the total
The sample mean is a point of estimator of the population mean
N is the no. of observations in a population
The μ is symbol for a population mean
, 2. Median = A measure of central location provided by the value in the middle when the data are
arranged in ascending order (smallest to largest).
- Odd numbers has a middle value
- Even numbers have a single middle value (x + x/2)
3. Mode = A measure of location, defined as the value that occurs with greatest frequency.
- Bimodal = if the data contains exactly two modes
- Multimodal = if data contains more than two modes
Excel Functions:
Mean = AVERAGE(B2:B13)
Median = MEDIAN(B2:B13)
Mode = MODE.SNGL(B2:B13)
4. Weighted Mean = the mean obtained by assigning each observation a weight that reflects its
importance.
Where wi is weight for observation i
When data is from sample: x bar
When data is from population: μ
5. Geometric Mean = A measure of location that is calculated by finding the nth root of the
product of n values. It is applied to find the mean rate of change over quarters, months, weeks,
and even days
Function: used to analyse growth rates in financial data (average mean in this case will be
misleading)
Excel function:
For growth rate =1+.01*B2
Geometric mean = GEOMEAN(C2:C11)
