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Measures of Central Tendency. FLORINDA M SOLIMAN TEACHER II. TAGAYTAY CITY SCIENCE NATIONAL HIGH SCHOOL. Measures of Central Tendency. A measures of central tendency may be defined as single expression of the net result of a complex group.

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Measures of central tendency

Measures of Central Tendency




Measures of central tendency1
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

Measures of Central Tendency

  • There are three averages or measures of central tendency

  • Mean

  • Mode

  • Median

Measures of central tendency2
Measures of Central Tendency

  • 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

Measures of central tendency3
Measures of Central Tendency


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

Measures of central tendency4
Measures of Central Tendency

  • Limitations

  • In the absence of actual data it can mislead

  • Abnormal difference between the highest and the lowest score would lead to fallacious conclusions

  • A mean sometimes gives such results as appear almost absurd. e.g. 4.3. children

  • Its value cannot be determined graphically

Measures of central tendency5
Measures of Central Tendency

Steps in Constructing Frequency Distribution Table

  • 1. Range = Highest Score – Lowest Score

  • 2. Class Width =

Chona s cupino teacher ii

Chona S. CupinoTEACHER II


for Mean

Amadeo National High School

Calculation of Arithmetic Mean

For Group Data

Assume mean Method:

Mean = AM +

Measures of central tendency6
Measures of Central Tendency

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

Measures of central tendency7
Measures of Central Tendency

Mean = AM +



= 29.5 +


= 28.3

Jocelyn c espineli teacher iii

Jocelyn C. EspineliTeacher III


for Median

Amadeo National High School

Measures of central tendency8
Measures of Central Tendency

  • 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.

Measures of central tendency9
Measures of Central Tendency

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

  • 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

Measures of central tendency10
Measures of Central Tendency

Median = L +

Here; L = 27.5 F = 35 fm =10

(40 – 35)


= 27.5 +


= 27.5 + 2

= 29.5

Variability standard deviation

VariabilityStandard Deviation





  • The goal for variability is to obtain a measure

    of how spread out the scores are in a


  • A measure of variability usually accompanies

    a measure of central tendency as basic

    descriptive statistics for a set of scores.

Central tendency and variability
Central Tendency and Variability

  • 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.


  • 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


  • In the context of inferential statistics,

    variability provides a measure of how

    accurately any individual score or sample

    represents the entire population.


  • 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.

Measuring variability
Measuring Variability

  • Variability can be measured with

    • the range

    • the interquartile range

    • the standard deviation/variance.

  • In each case, variability is determined

    by measuring distance.

The Standard Deviation

  • Standard deviation measures the

    standard distance between a score

    and the mean.

  • The calculation of standard deviation

    can be summarized as a four-step


The standard deviation table
The Standard Deviation Table

  • Compute the deviation

    (distance from the mean) for

    each score.

  • Solve for the product of

    frequency and deviation and

    solve for the total frequency


The standard deviation
The Standard Deviation

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

The standard deviation formula
The Standard Deviation Formula

SD =

SD =

SD = 4 ( 2.879) = 11.52

Means percentage score

Means Percentage Score


Master Teacher – I


How to Convert a Mean Score to a Percentage

  • 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.

How to Convert a Mean Score to a Percentage

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.

How to convert a mean score to a percentage
How to Convert a Mean Score to a Percentage

  • Instructions

  • 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.

How to convert a mean score to a percentage1
How to Convert a Mean Score to a Percentage

  • 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.

How to convert a mean score to a percentage2
How to Convert a Mean Score to a Percentage

  • Instructions

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

How to convert a mean score to a percentage3
How to Convert a Mean Score to a Percentage

  • 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.