EDUC 316:ASSESSMENT OF LEARNING I

MEASURES OF CENTRAL TENDENCY

Marikina Polytechnic College1st Semester, A.Y. 2015 - 2016

MEASURE OF CENTRAL TENDENCY

The measure of central tendency is populary known as an average, where as ingle central value can stand for the entire group of figures as typical of all the values in the group, these are:

1. Mean2. Median3. Mode

MEAN

Mean is the most frequently used measure of central tendency because it is subject to less error; it is also easily calculated.

MEAN

ADVANTAGE DISADVANTAGE best measure for regular distribution

does not supply information about the homogeneity of the group

The ARITHMETIC MEAN

The symbol , called “X bar” is used to represent the mean of a sample and the symbol , called “mu”, is used to denote the mean of a population.

X

Mean of Ungrouped Data

MeanSum of all the scores

Number of scores or cases

1 2 3 ... kX X X XX

N

where:

Mean of Ungrouped Data

XX

N

Arithmetic mean

Sum of all the scores

Number of scores or cases

X

X

N

The weighted mean is applicable to options of different weights. It is found by multiplying each value by its corresponding weight and dividing by the sum of weights.

The WEIGHTED MEAN

Weighted Mean

1 1 2 2 3 3

1 2 3

... ...

k kf

k

f X f X f X f XXf f f f

where: weighted mean

Sum of all the products of and

where is the frequency of each scoreand , weight of each scoreSum of all the respondents tested

observations

fX

fX f X

fX

f

18 14 12 10 9 718 13 12 10 8 717 13 11 10 8 616 12 11 10 8 515 12 11 9 8 3

Samples of 30 college students are considered for study with Math quiz score out of 20 points. Compute the mean, median, and mode of the data.

Mean of Grouped Data

Mean

Sum of all the product of midpoint times frequency

Total number of cases

fMX

N

Arithmetic mean using the midpoint method. The steps are as follows:Step 1: Compute the midpoints of all class

limits which is given the symbol M.Step 2: Multiply each midpoint by the

corresponding frequency.Step 3: Sum of the product of midpoints times

frequencies.Step 4: Divide this sum by the total number of

cases (N) to he obtain mean.

18 14 12 10 9 718 13 12 10 8 717 13 11 10 8 616 12 11 10 8 515 12 11 9 8 3

Construct a frequency distribution and compute the mean, median and mode of the data.

MEDIAN

The sum of absolute deviations (disregard the sign) ∑d about the median is less than or equal to the sum of absolute deviations about any other value.

Median is consistent in type with other point measures such as the quartile, decile, and percentile.

MEDIAN

ADVANTAGE DISADVANTAGE best measure of central tendency when the distribution is irregular or skewed.

necessitates arranging of items according to size before it can be computed

MEDIAN from Ungrouped Data

To determine the value of median for ungrouped data, we need to consider two rules:1. If n is odd, the median is the middle

ranked.2. If n is even, then the median is the average of two middle ranked values.Note that n the population/sample size.

MEDIAN from Ungrouped Data

( 1)Median ( Ranked Value) = 2

Note that is the population/sample size.

n

n

MEDIAN from Grouped Data

The median is located in the middle value of the frequency distribution. It is the value that separates the upper half of the distribution from the lower half. It is also a measure of central tendency because it is the exact center of the scores in a distribution.

MEDIAN from Grouped Data

medianlower real limit of the median classotal number of cases

um of the cumulative frequencies "lesser than"

up to but below the median classfrequency of the median classcla

XLN t

Cf s

fCC

ss interval

2N C f

x L Cf C

where:

MODE

It is the value in a data set that appears most frequently. In a data set, extreme values do not affect the mode. A data may not contain any mode if none of the values is “most typical”.

MODE

ADVANTAGE DISADVANTAGE always a real value since it does not fall on zero

inapplicable to small number of cases when the values may not be repeated

MODE from Ungrouped Data

A data set that has only one value that occurs with the greatest frequency is said to be unimodal.

If a data set has two values that occur with the same greatest frequency, both values are considered to be the mode and the data set is said to be bimodal.

MODE from Ungrouped Data

If a data set has more than two values that occur with the same greatest frequency, each value is used as the mode, and the data set is said to be multimodal.

When no data value occurs more than once, the data set is said to have no mode.

MODE from Grouped Data 1 2

0 2 12 2mof fCX Lf f f

1

2

0

modelower class limit of modal classfrequency of the class after the modal classfrequency of the class before the modal classfrequency of the modal classclass interval

XLfffC

where: