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Estimation of Parameters
Statistics and Probability

Descripted measures computed from a sample.
Statistic
Parameters
Descripted measures computed from a population.

1. What do we call a process by which
one makes inferences about a population
based on observation obtained from a
sample?

2. What do we call the value or range of
values used to approximate a parameter?

3. What are the types of population
Estimate?

1. What do we call a process by which
one makes inferences about a population
based on observation obtained from a
sample?
----ESTIMATION----
-Process used to calculate the population
parameters by analyzing only a small
random sample from the population

2. What do we call the value or range of
values used to approximate a parameter?
----ESTIMATE----

3. What are the types of population Estimate?
A. Point Estimate
B. Interval Estimate

A. Point Estimate
-a point estimate of a population parameter
is a single value of a statistics

B. Interval Estimate
-range of values within which the parameter
values possibly falls.

Point Estimate
-it is used to represent the true value of
a parameter.
--Example--
 sample mean estimates of the population mean.
 Sample variance estimates the population variance.
𝑥 =
𝑥
𝑛
𝑠2
=
𝑥 − 𝑥 2
𝑛 − 1

Point Estimate
A researcher wants to estimate the average grade
of all mathematics students in Saint Joseph
Institute of Technology. He determined the grades
of five students as follows; 76, 82, 88, 90 & 96.
Estimate the average mathematics grades of all
the students and the variance of their grades.
𝑥 =
𝑥
𝑛
𝑠2
=
𝑥 − 𝑥 2
𝑛 − 1
𝜎𝑚 =
𝜎
𝑛

Point Estimate
A researcher wants to estimate the average grade of all
mathematics students in Saint Joseph Institute of
Technology. He determined the grades of five students as
follows; 76, 82, 88, 90 & 96. Estimate the average
mathematics grades of all the students and the variance of
their grades.
𝑥 =
𝑥
𝑛
𝑥 =
76 + 82 + 88 + 90 + 96
5
𝑥 =
432
5
𝑥 = 86.4 ∴ 𝒕𝒉𝒆 𝒆𝒔𝒕𝒊𝒎𝒂𝒕𝒆 𝒑𝒐𝒑𝒖𝒍𝒂𝒕𝒊𝒐𝒏 𝒎𝒆𝒂𝒏 𝒊𝒔 𝟖𝟔. 𝟒

Point Estimate
𝑠2 =
𝑥 − 𝑥 2
𝑛 − 1
𝑠2
=
76 − 86.4 2
+ 82 − 86.4 2
+ 88 − 86.4 2
+ 90 − 86.4 2
+ 96 − 86.4 2
5 − 1
𝑠2
=
−10 2
+ −4.4 2
+ 1.6 2
+ 3.6 2
+ 9.6 2
4
𝑠2 =
108.16 + 19.36 + 2.56 + 12.96 + 92.16
4
𝑠2 =
235.2
4
𝑠2
= 58.8
𝑻𝒉𝒖𝒔, 𝒕𝒉𝒆 𝒆𝒔𝒕𝒊𝒎𝒂𝒕𝒆 𝒐𝒇 𝒕𝒉𝒆 𝒑𝒐𝒑𝒖𝒍𝒂𝒕𝒊𝒐𝒏 𝒗𝒂𝒓𝒊𝒂𝒏𝒄𝒆 𝒊𝒔 𝟓𝟖. 𝟖

Point Estimate
What is the best point estimate of the population
mean 𝜇 if a sample consisting of
19, 20, 26, 29, 𝑎𝑛𝑑 36 and is obtained from the
population?
𝑥 =
𝑥
𝑛
𝑠2 =
𝑥 − 𝑥 2
𝑛 − 1
𝜎𝑚 =
𝜎
𝑛

Point Estimate
What is the best point estimate of the population
mean 𝜇 if a sample consisting of
19, 20, 26, 29, 𝑎𝑛𝑑 36 and is obtained from the
population?
𝑥 =
𝑥
𝑛
𝑥 =
19 + 20 + 26 + 29 + 36
5
𝑥 =
130
5
𝑥 = 26
∴ 𝒕𝒉𝒆 𝒃𝒆𝒔𝒕 𝒑𝒐𝒊𝒏𝒕 𝒆𝒔𝒕𝒊𝒎𝒂𝒕𝒆 𝒐𝒇 𝒕𝒉𝒆 𝒑𝒐𝒑𝒖𝒍𝒂𝒕𝒊𝒐𝒏 𝒎𝒆𝒂𝒏 𝒊𝒔 𝟐𝟔

Point Estimate
A sample consisting of 12,14,18,22 𝑎𝑛𝑑 24 is used to
estimate the population mean 𝜇 . What is the
standard error of the point estimate of the
population mean 𝜇 when the population standard
deviation is estimated to be 𝜎 = 3.25?
𝑥 =
𝑥
𝑛
𝑠2 =
𝑥 − 𝑥 2
𝑛 − 1
𝜎𝑚 =
𝜎
𝑛

Point Estimate
A sample consisting of 12,14,18,22 𝑎𝑛𝑑 24 is used to
estimate the population mean 𝜇 . What is the
standard error of the point estimate of the
population mean 𝜇 when the population standard
deviation is estimated to be 𝜎 = 3.25?
𝜎𝑚 =
𝜎
𝑛
𝜎𝑚 =
3.25
5
𝜎𝑚 =
3.25
2.24
𝜎𝑚 = 1.45 ∴ 𝒕𝒉𝒆 𝒔𝒕𝒂𝒏𝒅𝒂𝒓𝒅 𝒆𝒓𝒓𝒐𝒓 𝒐𝒇 𝒕𝒉𝒆 𝒑𝒐𝒊𝒏𝒕 𝒆𝒔𝒕𝒊𝒎𝒂𝒕𝒆 𝒊𝒔 𝟏. 𝟒𝟓

Point Estimate
𝑥 =
𝑥
𝑛 𝑠2 =
𝑥 − 𝑥 2
𝑛 − 1
𝜎𝑚 =
𝜎
𝑛

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