Presentation on theme: "Measures of Central Tendency"— Presentation transcript:
1 Measures of Central Tendency FLORINDA M SOLIMANTEACHER IITAGAYTAY CITY SCIENCE NATIONAL HIGH SCHOOL
2 Measures of Central Tendency A measures of central tendency may be defined as single expression of the net result of a complex group.There are two main objectives for the study of measures of Central Tendency.To get one single value that represents the entire data.To facilitate comparison
3 Measures of Central Tendency There are three averages or measures of central tendencyMeanModeMedian
4 Measures of Central Tendency Mean/Arithmetic MeanThe most commonly used and familiar index of central tendency for a set of raw data or a distribution is the meanThe mean is simple Arithmetic AverageThe arithmetic mean of a set of values is their sum divided by their number
5 Measures of Central Tendency MERITS OF THE USE OF MEANIt is easy to understandIt is easy to calculateIt utilizes entire data in the groupIt provides a good comparisonIt is rigidly defined
6 Measures of Central Tendency LimitationsIn the absence of actual data it can misleadAbnormal difference between the highest and the lowest score would lead to fallacious conclusionsA mean sometimes gives such results as appear almost absurd. e.g childrenIts value cannot be determined graphically
7 Measures of Central Tendency Steps in Constructing Frequency Distribution Table1. Range = Highest Score – Lowest Score2. Class Width =
8 Scores of 80 students494844474640434241363738393233343528293025242627202122231617191213141589107494844474640434241363738393233343528293025242627202122231617191213141589107
9 Frequency Distribution CLASS INTERVALS ( CI )FREQUENCY ( F )n8048 – 51n8044 – 478040 – 438036 – 398032 – 35n8028 – 318024 – 278020 – 238016 – 19n8012 – 15808 – 11n804 – 7n80
10 Frequency Distribution CLASS INTERVALS ( CI )FREQUENCY ( F )n8048 – 512n8044 – 47540 – 4378036 – 39108032 – 3511n8028 – 31108024 – 2788020 – 2398016 – 194n8012 – 155808 – 116n804 – 73n80
11 Chona S. Cupino TEACHER II Calculationfor MeanChona S. Cupino TEACHER IIAmadeo National High School
12 Calculation of Arithmetic Mean For Group Data Assume mean Method: Mean = AM +
13 Measures of Central Tendency Calculation of Arithmetic Mean For Group DataX = midpointAM = Assumed Meani = Class Interval sizefd = Product of the frequency and the corresponding deviation
19 Class Intervals( CI )Frequency ( F )<CfMdptd’fd’48 – 5228049.551044 – 477845.542040 – 4377341.532136 – 396637.532 – 35115633.5128 – 314529.524 – 2783525.5-1-892721.5-2-1816 – 191817.5-3-1212 – 151413.5-4-208 – 1169.5-5-304 - 75.5-6Total-24
20 Measures of Central Tendency Mean = AM +(-24)80=4= 28.3
21 Jocelyn C. Espineli Teacher III Calculationfor MedianJocelyn C. Espineli Teacher IIIAmadeo National High School
22 Measures of Central Tendency MedianWhen all the observation of a variable arearranged in either ascending or descendingorder the middles observation is Median.It divides the whole data into equalproportion. In other words 50% observationswill be smaller than the median and 50% willbe larger than it.
23 Measures of Central Tendency Merits of MedianLike mean, Median is simple to understandMedian is not affective by extreme itemsMedian never gives absurd or fallacious resultMedian is specially useful in qualitative phenomena
24 Median = L +Where,L = exact lower limit of the Cl in whichMedian liesF = Cumulative frequency up to the lower limit of the Cl containing Medianfm = Frequency of the Cl containing mediani = Size of the class intervals
26 Measures of Central Tendency Median = L +Here; L = F = 35 fm =10(40 – 35)10=4== 29.5
27 Variability Standard Deviation MARILOU M. MARTINTEACHER - 1IMUS NATIONAL HIGH SCHOOL
28 Variability The goal for variability is to obtain a measure of how spread out the scores are in adistribution.A measure of variability usually accompaniesa measure of central tendency as basicdescriptive statistics for a set of scores.
29 Central Tendency and Variability Central tendency describes the central pointof the distribution, and variability describeshow the scores are scattered around thatcentral point.Together, central tendency and variability arethe two primary values that are used todescribe a distribution of scores.
30 Variability Variability serves both as a descriptive measure and as an important componentof most inferential statistics.As a descriptive statistic, variabilitymeasures the degree to which the scoresare spread out or clustered together in adistribution.In the context of inferential statistics,variability provides a measure of howaccurately any individual score or samplerepresents the entire population.
31 Variability When the population variability is small, all of the scores are clustered close togetherand any individual score or sample willnecessarily provide a good representationof the entire set.On the other hand, when variability is largeand scores are widely spread, it is easy forone or two extreme scores to give adistorted picture of the general population.
32 Measuring Variability Variability can be measured withthe rangethe interquartile rangethe standard deviation/variance.In each case, variability is determinedby measuring distance.
33 The Standard Deviation Standard deviation measures thestandard distance between a scoreand the mean.The calculation of standard deviationcan be summarized as a four-stepprocess:
34 The Standard Deviation Table Compute the deviation(distance from the mean) foreach score.Solve for the product offrequency and deviation andsolve for the total frequencydeviation.
35 The Standard Deviation Compute for the sum of the product of frequency deviation square.(fd’²)
37 The Standard Deviation Formula SD =SD =SD = 4 ( 2.879) =
38 Means Percentage Score SHIRLEY PEL – PASCUALMaster Teacher – IGOV. FERRER MEMORIAL NATIONAL HIGH SCHOOL
39 How to Convert a Mean Score to a Percentage Mean scores are used to determinethe average performances ofstudents or athletes, and in variousother applications.Mean scores can be converted topercentages that indicate theaverage percentage of the scorerelative to the total score.
40 How to Convert a Mean Score to a Percentage Mean scores can also be converted topercentages to show the performanceof a score relative to a specific score.For instance, a mean score can becompared to the highest score with apercentage for a better comparison.Percentages can be useful means ofstatistical analysis.
42 How to Convert a Mean Score to a Percentage InstructionsFind the mean score if not already determined.The mean score can be determined by addingup all the scores and dividing it by "n," thenumber of scores.
43 How to Convert a Mean Score to a Percentage Instructions2 Determine the score that you want to compare the mean score to. You may compare the mean score with the highest possible score, the highest score, or a specific score.
44 How to Convert a Mean Score to a Percentage Instructions3. Divide the mean score by the score you decided to use in step 2.
45 How to Convert a Mean Score to a Percentage Instructions4. Multiply the decimal you obtain instep 3 by 100, and add a % sign toobtain the percentage. You maychoose to round the percentage tothe nearest whole number.