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Measures of Central Tendency

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### Measures of Central Tendency

### Means Percentage Score

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.

- 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

- There are three averages or measures of central tendency

- Mean

- Mode

- Median

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 Tendency

- 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

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 Tendency

Steps in Constructing Frequency Distribution Table

- 1. Range = Highest Score – Lowest Score

- 2. Class Width =

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 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 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 Tendency

Median = L +

Here; L = 27.5 F = 35 fm =10

(40 – 35)

10

= 27.5 +

4

= 27.5 + 2

= 29.5

Variability

- 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.

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

- 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.

Variability

- 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

- Variability can be measured with
- the range
- the interquartile range
- the standard deviation/variance.

- In each case, variability is determined
by measuring distance.

- 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:

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

deviation.

The Standard Deviation

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

SHIRLEY PEL – PASCUAL

Master Teacher – I

GOV. FERRER MEMORIAL NATIONAL HIGH SCHOOL

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

- 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 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 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 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.

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