Statistics and Probability

1. SAMPLING
PRESENATION 2

2. Sample
 A subset that represents the general traits
or characteristics of the large group
(population).
 Subset

3. Simple Random Sampling
 The common method used to do sampling.
 Simple Random Sampling with
Replacement
 Simple Random Sampling without
Replacement

4. Parameter vs. Statistic
 Statistic is a measurement that describes a
sample
 Parameter is a measurement that
describes the whole population.

5. Parameter vs. Statistic
 EXAMPLES:
 If a bunch lanzones taken from a box
is 90% sweet. (statistic)
 If all applicants taking the SHS
Entrance Test were asked how they
feel and 75% said they are nervous.
(parameter)

6. Parameter vs. Statistic
 PRACTICE:
 All 550 churchgoers were asked
their preferences for a barangay
venue for Christmas celebration.
Sixty percent preferred the barangay
hall to serve as venue.

7. Parameter vs. Statistic
 PRACTICE:
 There are 10 of the basketball
games played during the year that
had a mean total score of 152
between the opposing teams.

8. Parameter vs. Statistic
TRY This!
Determine whether the
situation tells about a statistic
and parameter.
#1-5 page ___

9. Identifying Sampling Distributions

10. Central Limit Theorem (CLT)
 The distribution of the means of the
numerous samples form a normal
distribution.
x
n

 
x
 

11. Mean of the Sampling
Distribution of the Means
x
 

12. Variance of the Sampling
Distribution of the Means
2
2
x
n

 

13. Example 1
 Our hypothetical population contains
the scores 4, 6, 7, and 9. Determine
the mean and variance of the
sampling distribution of the sample
mean, given that the samples contain
two scores drawn from a population
with replacement.

14. Frequency Distribution Table
Mean Frequency
4.0 I
4.5
5.0 II
5.5 II
6.0 I
6.5 IIII
7.0 I
7.5 II
8.0 II
8.5
9.0 I

15. Frequency Distribution Table
Mean Frequency Probability
4.0 I 1/16
4.5
5.0 II 1/8
5.5 II 1/8
6.0 I 1/16
6.5 IIII ¼
7.0 I 1/16
7.5 II 1/8
8.0 II 1/8
8.5
9.0 I 1/16

16. Probability Histogram
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9

17. Central Limit Theorem
 For a population with a finite mean
μ and a finite non-zero variance σ2
, the sampling distribution of the
mean approaches a normal
distribution with a mean of μ and a
variance of σ2 / n as the sample n
increases.

18. Central Limit Theorem
20x 
5n 
15n 
25n 

19. Standard Error
 The standard deviation of the
sampling distribution of the
sample means.

20. Example 2:
 Suppose a population has mean 80 and
standard deviation 10. Then we get a
sample of 90 cases and the mean of this
sample is 82. how frequently does the
sample 90 cases differ by 2 or more points
from the population mean?

21. Example 3:
 The mean height of the Grade V students is
students is 148cm with a standard deviation of
8 cm. A sample of 30 students is taken and the
mean height of the sample is 145cm. What is
the probability that the sample of 30 students
has a mean height that differs by 2 cm or less
from the population mean?

22. Example 4:
 The mean weigh of a banana is 92 g with a sd
of 6 g. A sample of 36 is taken from a basket
and the mean weight of the sample is 94 g.
What is the probability that this sample has a
mean weight that differs by 2 g or more than
population mean?