DESCRIBING DATA = NUMERICAL MEASURES =

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

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

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

SORTS OF MEAN Arithmetic Mean Geometric Mean Harmonic Mean

ARITHMETIC MEAN

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?

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?

WEIGHTED MEAN

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.

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?

ARITH. MEAN OF GROUPED DATA

EXAMPLE: MEAN OF GROUPED DATA AGE OF INTERNET USERS IN A CERTAIN COMMUNITY NO. AGE (years old) FREQUENCY 1 22 - 26 5 2 27 - 31 13 3 32 - 36 17 4 37 - 41 25 42 - 46 20

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.

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

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

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

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

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

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.

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.