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FLORINDA M SOLIMAN TEACHER II TAGAYTAY CITY SCIENCE NATIONAL HIGH SCHOOL

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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 facilitate comparison To get one single value that represents the entire data.

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There are three averages or measures of central tendency Mean Median Mode

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Mean/Arithmetic Mean The most commonly used and familiar index of central tendency for a set of raw data or a distribution is the mean The mean is simple Arithmetic Average The arithmetic mean of a set of values is their sum divided by their number

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MERITS OF THE USE OF MEAN It is easy to understand It is easy to calculate It utilizes entire data in the group It provides a good comparison It is rigidly defined

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Limitations Abnormal difference between the highest and the lowest score would lead to fallacious conclusions In the absence of actual data it can mislead Its value cannot be determined graphically A mean sometimes gives such results as appear almost absurd. e.g children

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Steps in Constructing Frequency Distribution Table 1. Range = Highest Score – Lowest Score 2. Class Width =

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CLASS INTERVALS ( CI )FREQUENCY ( F ) n80 48 – 51 n80 44 – – – – 35 n80 28 – – – – 19 n80 12 – – 11 n80 4 – 7 n80

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CLASS INTERVALS ( CI )FREQUENCY ( F ) n80 48 – 51 2 n80 44 – – – – 3511 n80 28 – – – – 194 n80 12 – – 116 n80 4 – 73 n80

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Calculation for Mean

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Calculation of Arithmetic Mean For Group Data Assume mean Method: Mean = AM +

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Calculation of Arithmetic Mean For Group Data X = midpoint AM = Assumed Mean i = Class Interval size fd = Product of the frequency and the corresponding deviation

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Class Intervals ( CI ) Frequency ( F ) 48 – – – – – – – – – – Total80 Class Intervals ( CI ) Frequency ( F )

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Class Intervals ( CI ) Frequency ( F )

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Class Intervals ( CI ) Frequency ( F )

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Class Intervals ( CI ) Frequency ( F )

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Class Intervals ( CI ) Frequency ( F )

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Class Intervals ( CI ) Frequency ( F )

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Mean = AM + = (-24) 80 4 = 28.3

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Calculation for Median

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Median When all the observation of a variable are arranged in either ascending or descending order the middles observation is Median. It divides the whole data into equal proportion. In other words 50% observations will be smaller than the median and 50% will be larger than it.

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Merits of Median Like mean, Median is simple to understand Median is not affective by extreme items Median never gives absurd or fallacious result Median is specially useful in qualitative phenomena

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Median = L + Where, L = exact lower limit of the Cl in which Median lies F = Cumulative frequency up to the lower limit of the Cl containing Median fm = Frequency of the Cl containing median i =Size of the class intervals

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Class Intervals ( CI ) Frequency ( F )

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Median = L + Here; L = 27.5 F = 35 fm =10 = (40 – 35) 10 4 = = 29.5

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MARILOU M. MARTIN TEACHER - 1 IMUS NATIONAL HIGH SCHOOL

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The goal for variability is to obtain a measure of how spread out the scores are in a distribution. A measure of variability usually accompanies a measure of central tendency as basic descriptive statistics for a set of scores.

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Central tendency describes the central point of the distribution, and variability describes how the scores are scattered around that central point. Together, central tendency and variability are the two primary values that are used to describe a distribution of scores.

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Variability serves both as a descriptive measure and as an important component of most inferential statistics. As a descriptive statistic, variability measures the degree to which the scores are spread out or clustered together in a distribution. In the context of inferential statistics, variability provides a measure of how accurately any individual score or sample represents the entire population.

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When the population variability is small, all of the scores are clustered close together and any individual score or sample will necessarily provide a good representation of the entire set. On the other hand, when variability is large and scores are widely spread, it is easy for one or two extreme scores to give a distorted picture of the general population.

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Variability can be measured with the range the interquartile range the standard deviation/variance. In each case, variability is determined by measuring distance.

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Standard deviation measures the standard distance between a score and the mean. The calculation of standard deviation can be summarized as a four-step process:

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1. Compute the deviation (distance from the mean) for each score. 2. Solve for the product of frequency and deviation and solve for the total frequency deviation.

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3. Compute for the sum of the product of frequency deviation square.(fd ²)

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Class Intervals ( CI ) Frequency ( F )

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SD = SD = 4 ( 2.879) = 11.52

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SHIRLEY PEL – PASCUAL Master Teacher – I GOV. FERRER MEMORIAL NATIONAL HIGH SCHOOL

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Mean scores are used to determine the average performances of students or athletes, and in various other applications. Mean scores can be converted to percentages that indicate the average percentage of the score relative to the total score.

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Mean scores can also be converted to percentages to show the performance of a score relative to a specific score. For instance, a mean score can be compared to the highest score with a percentage for a better comparison. Percentages can be useful means of statistical analysis.

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Instructions 1. Find the mean score if not already determined. The mean score can be determined by adding up all the scores and dividing it by "n," the number of scores.

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Instructions 2 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.

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Instructions 3. Divide the mean score by the score you decided to use in step 2.

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Instructions 4. Multiply the decimal you obtain in step 3 by 100, and add a % sign to obtain the percentage. You may choose to round the percentage to the nearest whole number.

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