ppt on statistics and probability

1. SAMPLING
DISTRIBUTI
ON

2. ACTIVITY 1:
SHOW ME ACT
ME!

3. ACTIVITY 2: HOW DO YOU KNOW
ME!
•A RESEARCHER WANTS TO ESTIMATE
THE AVERAGE MONTHLY ALLOWANCE
OF THE GRADE 11 FEMALE STUDENTS.
FROM A RANDOM SAMPLE OF 50
FEMALE STUDENTS, THE RESEARCHER
OBTAINS A SAMPLE MEAN MONTHLY
ALLOWANCE OF 75 PESOS

4. ACTIVITY 3: COMPUTE FOR THE
MEAN OF THE SET OF NUMBERS
BELOW. ROUND OFF YOUR ANSWERS
TO TWO DECIMAL PLACES.
1.) 3, 6, 8,4, 10
2.) 6, 8, 16, 18, 20, 22
3.) 31, 36, 30, 35, 38, 41, 44, 37, 39

5. ACTIVITY 4:
A POPULATION CONSISTS OF THE
FOUR NUMBERS 1, 2, 8, AND 9. LIST
ALL THE POSSIBLE SAMPLES OF SIZE N
= 2 WHICH CAN BE DRAWN WITH
REPLACEMENT FROM THE
POPULATION. AND COMPUTE THE

8. • PARAMETER A MEASURE THAT DESCRIBES A
POPULATION. IT IS A NUMBER THAT DESCRIBES
SOME CHARACTERISTIC OF THE POPULATION. IN
STATISTICAL PRACTICE, THE VALUE OF A
PARAMETER IS USUALLY NOT KNOWN BECAUSE WE
CANNOT EXAMINE THE ENTIRE POPULATION.
• STATISTIC A MEASURE THAT DESCRIBES A
SAMPLE. IT IS A NUMBER THAT DESCRIBES SOME
CHARACTERISTIC OF A SAMPLE. THE VALUE OF A
STATISTIC CAN BE COMPUTED DIRECTLY FROM
THE SAMPLE DATA. WE USE A STATISTIC TO

9. SYMBOLS: PARAMETERS AND
STATISTICS
Proportions Means
Standard
Deviation
Statistic s
Parameter P µ

10. EXAMPLE:
A TEACHER WANTS TO KNOW THE AVERAGE HOURS SPEND
ON SOCIAL MEDIA OF HIS ADVISORY CLASS. HE
RANDOMLY SELECTED AND ASKED 35 STUDENTS AND
FOUND OUT THAT THEY SPEND AN AVERAGE OF 3 HOURS
PER DAY ON SOCIAL MEDIA.
• PARAMETER: THE AVERAGE HOURS SPEND ON SOCIAL
MEDIA OF HIS ADVISORY CLASS.
• STATISTIC: AN AVERAGE OF 3 HOURS PER DAY FROM A
SAMPLE OF 35 STUDENTS SPEND ON SOCIAL MEDIA.

11. SAMPLING DISTRIBUTION
•THE SAMPLING DISTRIBUTION OF
A STATISTIC IS THE
DISTRIBUTION OF VALUES TAKEN
BY THE STATISTIC IN ALL
POSSIBLE SAMPLES OF THE SAME
SIZE FROM THE SAME

12. FINDING THE MEAN AND VARIANCE OF THE
SAMPLING DISTRIBUTION OF THE SAMPLE
MEANS

13. EXAMPLE: CONSIDER A POPULATION CONSISTING OF THE
VALUES 2, 5, 8.
• COMPUTE FOR THE POPULATION MEAN
• COMPUTE THE POPULATION VARIANCE
• FIND THE POPULATION STANDARD DEVIATION
• LIST ALL THE POSSIBLE SAMPLE SIZE OF N = 2 WITH
REPLACEMENT AND CORRESPONDING MEANS
• FIND THE MEAN OF THE SAMPLING DISTRIBUTION
• FIND THE VARIANCE OF THE SAMPLING DISTRIBUTION OF
SAMPLE MEANS
• FIND THE STANDARD DEVIATION OF THE SAMPLING

14. IDENTIFY WHETHER THE GIVEN VALUE IS A PARAMETER OR A STATISTIC.
• THE RESEARCHER FOUND OUT THAT THE 29 STUDENTS SENIOR HIGH
SCHOOL TEACHERS OF A CERTAIN SCHOOL SPEND AN AVERAGE OF 2
HOURS PREPARING THEIR LESSONS
• BASED ON A SAMPLE OF 900 ELEMENTARY STUDENTS, IT WAS FOUND
OUT 30% OF THEM DO NOT KNOW MULTIPLICATION FACTS.
• BASED ON SAMPLE OF 1,200 SURVEYED STUDENTS, IT WAS FOUND OUT
THAT 205 OF THEM NEEDED FINANCIAL ASSISTANCE.
• A TEACHER SURVEYED ALL 50 STUDENTS UNDER HIS ADVISORY CLASS
ABOUT THEIR LEARNING STYLES AND FOUND OUT THAT MOST OF THEM
ARE VISUAL LEARNERS
• THE STATISTICS TEACHER WANTS TO KNOW THE AVERAGE SCORE OF
THE STUDENTS IN THE FINAL EXAM. HE RANDOMLY SELECTED 35
STUDENTS AND OBTAINED AN AVERAGE SCORE OF 43.

15. STUDY THE CASE BELOW AND ANALYZE WHETHER IT
EMPHASIZES PARAMETER OR STATISTIC.
• A RESEARCHER RANDOMLY SELECTED A SAMPLE OF 1600
SAMPLE PEOPLE IN CAGAYAN DE ORO CITY AND ASKED IF
THEY USE A BURNER AND 40% OF THEM SAID YES.
• A RESEARCHER INTERVIEWED ALL THE MEMBERS OF THE
SHS DEPARTMENT. HE WANTS TO KNOW THE AVERAGE
HOURS PER DAY THEY SPEND IN TRAINING THEIR
STUDENTS FOR COMPETITION AND FOUND OUT THAT
THEY SPEND AN AVERAGE OF 5 HOURS PER DAY FOR
TRAINING.

17. QUIZ

18. SOLVE THE PROBLEM BELOW.
CONSIDER ALL SAMPLES OF SIZE OF 5 FROM THIS POPULATION: 2, 5,
7, 9, 10, 11, 12
• COMPUTE THE POPULATION MEAN
• COMPUTE THE POPULATION VARIANCE
• COMPUTE THE POPULATION STANDARD DEVIATION
• COMPUTE THE MEAN OF THE SAMPLING DISTRIBUTION OF THE
SAMPLE MEANS
• COMPUTE THE VARIANCE OF THE SAMPLING DISTRIBUTION OF THE
SAMPLE MEANS
• COMPUTE THE STANDARD DEVIATION OF THE SAMPLING
DISTRIBUTION OF THE SAMPLE MEANS