The document discusses measures of central tendency, which are single values that represent typical behavior in a data set. There are three main types: the mean is the average found by summing all values and dividing by the number of data points; the median is the middle value when data is arranged from lowest to highest; and the mode is the most frequently occurring value. Examples are provided to demonstrate calculating the mean, median, and mode of various data sets.

1. Measures
of
Central Tendency

2. Measures of Central Tendency
- is any single value that is used to identify
the center of the data or the value.
- these measures provide information about
the average and typical behavior of the
language learners as regards the linguistic
elements being investigated.
- it is used to summarize data into a single
value.

3. Some Definitions
 Simpson and Kafka defined it as “a measure of
central tendency is a typical value around which
other figures gather.”
 Waugh has expressed “an average stand for the
whole group of which it forms a part yet
represents the whole.”
 In Layman’s term, a measure of central
tendency is an average. It is a single number of
value which can be considered typical in a set of
data as a whole.

4. Importance of Central Tendency
 To find representative value.
 To make more concise data.
 To make comparisons.
 It is helpful in further statistical
analysis.

5. 3 Types of Central Tendencies
 Mean
 Median
 Mode

6. Mean (X)
- is commonly called the average or the
arithmetic mean.
- it is the most popular and widely used.
- refers to the measure obtained
by adding all the scores of
respondents and dividing the
sum by the number of subjects.

7. Example #1
Mr. Jackson randomly selects ten students to
answer a questionnaire on the correct usage of
grammar. Scores for a sample of ten students are as
follows: 84, 75, 90, 98, 88, 79, 95, 86, 93, and 89.
Find the mean.
X = 84+75+90+98+88+79+95+86+93+89
10
= 877
10
X = 87.7 is the mean

8. Example #2
The number of pupils who speak English Language
at six different classrooms in MCC are as follows: 10,
10, 12, 14, 15, 20. Find the mean number of pupils who
speak English Language for the six different classrooms
in MCC.
X = 10+10+12+14+15+20
6
= 81
6
X = 13.5 is the mean number

9. Median (Md)
- is the score which divides the population
into two in which half of the scores are
above and half are below it.
- the midpoint of a data set.
- is calculated by arranging the
data set in order from least to greatest and
identify the middle number.
- is dependent on whether the
number of elements in the
data set is odd or even.

10. Example #1
Mr. Catulay conducted a vocabulary test in a
random sample of Grade VII students of MCC and
their scores out of 25 items are as follows: 19, 15,
22, 17, 21, 17, 25, 18, 17. Find the median.
15 17 17 17 18 19 21 22 25
Md = 18 is the median

11. Example #2
Find the median of the scores in English
vocabulary of Grade VII students of MCC in the
given data set: 19, 15, 22, 17, 21, 17.
15 17 17 19 21 22
Md = 17 + 19
2
= 36
2
Md = 18 is the median

12. Mode (Mo)
- refers to the scores which occurs most frequently
in the large group of respondents.
- it is the most unreliable among the three
measures of central tendency because its value is
undefined in some observations.
- it does not always exist, and if it does, it may not
be unique.
 Unimodal – one mode
 Bimodal – two modes
 Trimodal – three modes
 Multimodal – more than two
modes

13. Example #1
Identify the modes of the following data sets:
2, 5, 2, 3, 5, 2, 1
Mo = 2 is the mode

14. Example #2
The common errors in written English of the
students are as follows:
Correct Usage Spelling
Identifying Errors Mechanics
Tenses of the Verb Spelling
Word Usage Capitalization
Spelling Spelling
Mo = Spelling is the mode

16. ACTIVITY!!!
Choose the letter of the correct answer.
1. Which measure of central tendency
identifies the score that most
frequently occurs in a data set?
a. Mode c. Mean
b. Median d. Variance

17. 2. Which is the average score in the data set
calculated by summing all scores and then
dividing by the number of scores and is the
most commonly used measure of central
tendency?
a. Mode c. Mean
b. Median d. Variance

18. 3. You conducted a survey of students
in your school. You report that half
the students work 25 hours per
week or less. The statistic you used is
the ______.
a. Mean c. Mode
b. Median d. Variance

19. In a spelling test, some students
in a class scores: 13, 17, 12, 19, 20,
13, and 11 out of a total of 20.
Find their mean, median, and mode.