The document discusses estimation in statistics, specifically how to infer population parameters using sample data. It explains types of population estimates, such as point and interval estimates, and provides examples of calculating averages and variances for given student grades. The document also includes a formula for standard error when estimating the population mean.

1. Estimation of Parameters
Statistics and Probability

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

3. Questions

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

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

6. 3. What are the types of population
Estimate?

7. 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

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

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

10. 3. What are the types of population Estimate?
A. Point Estimate
-a point estimate of a population parameter
is a single value of a statistics

11. 3. What are the types of population Estimate?
B. Interval Estimate
-range of values within which the parameter
values possibly falls.

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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

19. 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

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

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

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