Stat 100 - Measures of Central Tendency PDF

STAT 100- Statistical Tools and Data Analysis INSTRUCTOR: GENARO T. ARDINA  Learning Objectives 1. Compute the mean, median and mode of the set of data 2. Identify the different properties of measures of central tendency;...

STAT 100- Statistical Tools and Data Analysis INSTRUCTOR: GENARO T. ARDINA  Learning Objectives 1. Compute the mean, median and mode of the set of data 2. Identify the different properties of measures of central tendency; PAGE 1  Teachers should know how to utilize these data, particularly in decision- Statistics plays a very making. important role in assessing Hence, a classroom teacher the performance of should have the necessary students, most especially in background in statistical describing and analyzing procedures in order for him to give a correct description their scores through and interpretation of assessment activities. students performance in a certain test, whether it is conducted by the teacher or the Department of Education or whether it is a division or a national PAGE 3 PAGE 2 assessment.  DEFINITION OF STATISTICS BRANCHES OF STATISTICS  Statistics is the branch of science that deals with the collection, DESCRIPTIVE INFERENTIAL organization, STATISTICS STATISTICS presentation, analysis and interpretation of quantitative data. Deals with collecting, describing, and analyzing set of data without drawing  Inductive Science conclusion Concerned with the analysis of a  Science of Variation subset of data leading to a predictions or inferences about PAGE 3 PAGE 2 the entire set of data without dealing with each individual in the population.  DESCRIBING GROUP MEASURES OF CENTRAL PERFORMANCE TENDENCY In describing the group perfor- mance of the students in a certain test, the measures of central Provides a very convenient way tendency and measures of varia- of describing a set of scores with bility are used. a single number that describes performance of a group. It is also Measures of Central Tendency are defined as a single value that is Used to determine the average used to describe the “center” Performance of the group scores, Of the data. While Measures of Variability indi- cate the spread of scores in a group MEAN. MEDIAN PAGE 5 PAGE 4 MODE  PROPERTIES PROPERTIES Used when the data are in Used when the data are in interval or in ratio level of ordinal level of measurement measurement MEDIAN- Used when the frequency Used when the frequency distribution is irregular, or refers to the distribution is regular, skewed. centermost symmetrical, or normal MEAN- refers score when Measures of stability the scores in Used when the middlemost to the the of the score is desired. arithmetic average Easily affected by extreme distribution scores Used when there are extreme are arranged scores Very easy to compute according to magnitude. Not affected by the extreme The sum of each score’s scores because it is positional distance from the mean is measures zero May not be an actual Used to compute other observation in the data set measures such as SD, CV, SK, PAGE 7 PAGE 6 and Z-score.  PROPERTIES TYPES OF MODE Used when the data are in nominal level of measurement Used when the quick answer  UNIMODAL= is a score MODE- refers is needed distribution consists of to the score/s one mode that occurs most Used when the score  BIMODAL= is a score distribution is normal distribution that consists frequently in the score Can be used for quantitative, of two modes. distribution as well as qualitative data  TRIMODAL= is a score distribution that consists May not be unique of three modes as MULTIMODAL= a score Not affected by extreme values distribution that consists of more than two modes. PAGE 9 PAGE 8 May not exist at times.  ILLUSTRATIVE EXAMPLE Mean for Ungrouped Data . The daily rates of sample of eight employees at GMS Inc. are P550, P420, P560, P500, P700, P670, P860, P480. Find the mean daily rate of the employee.  Find the population mean of the ages of 9 middle-management employees of a certain company. The ages are PAGE 11 PAGE 10 53, 45, 59, 48, 54, 46, 51, 58, and 55.  ILLUSTRATIVE EXAMPLE Mean for Grouped Data . Find the mean of the given data set below Class Limits f Midpoint (X) fx 18-26 3 22 66 27-35 5 31 155 36-44 9 40 360 45-53 14 49 686 54-62 11 58 638 63-71 6 67 402 72-80 2 76 152 PAGE 13 PAGE 12 50 2459  ILLUSTRATIVE EXAMPLE Weighted Mean It is particularly useful when . Last semester Miya took various classes or groups the following subjects; contribute differently to the total. SUBJECTS UNITS GRADE Math 101 3 90 The weighted mean is found by multiplying each value by its EED 005 3 88 corresponding weight and dividing EED 010 3 85 the sum of the weights. Hum 101 3 92 Engl. 101 3 94 Fil 101 3 94 PE 2 100 Find the weighted mean PAGE 15 PAGE 14 of her grades.  ILLUSTRATIVE EXAMPLE Geometric Mean The geometric mean of a set 1] Suppose the profits earned by MSS Construction Company on of n is defined as the nth root Five projects were 5, 6, 4, 8, and of the product of the n 10 percent, respectively. What is numbers. the geometric mean profit? 2] Badminton as sport grew rapidly in 2018. From January to December 2018 the number of badminton clubs in metro Manila increased from 20 to 155. Compute the monthly PAGE 17 PAGE 16 increase in the number of badminton clubs.  MEDIAN FOR UNGROUPED ILLUSTRATIVE EXAMPLE DATA The midpoint of the data array.  Find the median of the ages of 9 When the data is ordered whether middle-management employees ascending or descending , it is of a certain company. The ages called data array. are 53, 45, 59, 48, 54, 46, 51, 58, and 55. Step 1: Arrange the data in order Step2: Select the middle rank  The daily rates of sample of value. eight employees at GMS Inc. are 𝒏+𝟏 Median (rank value)= 𝟐 P550, P420, P560, P500, P700, P670, P860, P480. Find the Step 3: Identify the median in median daily rate of the PAGE 19 PAGE 18 the data set. employee.  MEDIAN FOR GROUPED Steps DATA Step 1: determine the median rank using the formula N/2. Step 2: Construct Cumulative frequency. Step 3: Identify the median Class Step 4: Determine the Value of LB, cf, f, i, and N. Step 5: Apply the formula PAGE 21 PAGE 20  ILLUSTRATIVE EXAMPLE Determine the median of the frequency distribution on the ages of people taking travel tours. Class Limits f cf Class Boundaries 18-26 3 3 27-35 i=9 5 8 36-44 9 Cf = 17 45-53 F= 14 31 44.5-53.5 (LB=44.5) 54-62 11 42 63-71 6 48 72-80 2 50 N= 50 PAGE 23 PAGE 22  EXERCISE EXERCISE The admission officer of a certain school conducted an entrance  What measure/s of test to 5 groups of students. In central tendency does the data shown below, find its the number 23 overall average. represent in the Group Number of Average following score Takers distribution: 30, 15, 20, A 10 90 23, 17, 23, 25, 27, 23? B 15 85 C 20 92 D 25 95 E 30 88 PAGE 25 PAGE 24 PAGE 26 END