1. DESCRIBING DATA
= NUMERICAL MEASURES =

2. TWO MEASURES IN STASTISTICS
Measures of Location/Central Tendencies
Measures of Dispersion

3. MEASURES OF LOCATION Mean Median Mode Quartiles Deciles Percentiles
What is the purpose of calculating mean or other measures of location?

4. MEASURES OF DISPERSION
Range
Quartile Deviation/Semi-Interquartile Range
Variance
Standard Deviation

5. SORTS OF MEAN
Arithmetic Mean
Geometric Mean
Harmonic Mean

6. ARITHMETIC MEAN

7. EXAMPLE 1: ARITHMETIC MEAN
In a certain study, 5 radio stations were taken as samples. Radio station A spent 80 minutes/day in commercial breaks, radio station B spent 90 minutes/day, C spent 100 minutes/day, D spent 75 minutes/day, and E spent 60 minutes/day. What was the sample mean of time spent in commercial breaks by the radio stations?

8. EXAMPLE 2: ARITHMETIC MEAN
A researcher conducted a study on advertising costs. He took a sample of 4 companies and their monthly advertising costs were $500, $750, $ 900, and $600. What was the mean monthly advertising cost?

9. WEIGHTED MEAN

10. EXAMPLE: WEIGHTED MEAN
MIDTEST : 30%
TASKS : 20%
FINAL TEST : 50%
A student got 60 for midtest, 90 for tasks, and 40 for final test. Calculate his mark on the subject.

11. QUIZ #1
The Loris Healthcare System employs 200 persons on the nursing staff. Fifty are nurse’s aides, 50 are practical nurses, and 100 are registered nurses. Nurse’s aides receive $8 an hour, practical nurses $15 an hour, and registered nurses $24 an hour. What is the mean hourly wage?

12. ARITH. MEAN OF GROUPED DATA

13. EXAMPLE: MEAN OF GROUPED DATA
AGE OF INTERNET USERS
IN A CERTAIN COMMUNITY
NO.
AGE (years old)
FREQUENCY 1 5 2 13 3 17 4 25 20

14. THE MEDIAN
is the midpoint of the values after they have been ordered from the smallest to the largest, or the largest to the smallest.
is not affected by extremely large or small values.
can be computed for ordinal-level data or higher.

15. HOW TO CALCULATE MEDIAN
Suppose X1, X2, X3, ..., Xn are the data with an increasing order (ordered from the smallest to the highest)
Let the median be Me
If n is odd, Me = Xk,where k = (n+1)/2
If n is even, Me = (Xn/2 + X1+n/2)/2

16. EXAMPLE 1: MEDIAN
Consider the following data: 13, 8, 25, 19, 39, 51, 4, 19, 45. Determine the median.

17. EXAMPLE 2: MEDIAN
Consider the following data: 13, 8, 25, 19, 39, 51, 4, 19, 45, 55. Determine the median.

18. QUIZ #2 No. Name GENDER Age (years) Education Level Cloth Size
Height (cm)
Fav Social Media 1 A M 23
SMA L
156 FB 2 B F 30 D3
167
Twitter 3 C 25 S1
149 4 D 42 XL
180 5 E 26 S
Line 6
Insta 7 G 34
SMP
161 8 H 43
160 9 I 32 S2
171 10 J 29
159 11 K 35
170

19. QUARTILES
Lower Quartile (Q1): the median of the lower half of the data
Upper Quartile (Q3): the median of the upper half of the data

20. HOW TO FIND THE LOWER QUARTILE
Suppose there are n data, ordered from the smallest to the largest: X1, X2, X3, ..., Xn.
Q1 = Xk, where k = (n+1)/4
If k is not a whole number, find the whole number t such that t < k < (t+1). Then Q1 is the weighted mean of Xt and Xt+1 using 3 and 1 as weights. If (k-t) < ((t+1)-k) then 3 is assigned to Xt. Otherwise, 3 is assigned to Xt+1.

21. HOW TO FIND THE UPPER QUARTILE
Suppose there are n data, ordered from the smallest to the largest: X1, X2, X3, ..., Xn.
Q3 = Xk, where k = 3(n+1)/4
If k is not a whole number, find the whole number t such that t < k < (t+1). Then Q3 is the weighted mean of Xt and Xt+1 using 3 and 1 as weights. If (k-t) < ((t+1)-k) then 3 is assigned to Xt. Otherwise, 3 is assigned to Xt+1.