17. Calculate mean from the following data:
f
2.
2
8
6
CI
90-94
85-89
80-84
75-79
70-74
65-69
60-64
55-59
50-54
45-49
40-44
11
9
7
52
0
25
N= 56
Answers
Answer:
UNIT 14 MEASURES OF CENTRAL Tendency
TENDENCY
Structure
14.1 Introduction
14.2 Objectives
14.3 Individual and Group Data
14.4 Measures of Central Tendency
14.4.1 Scales of Measurement and Measures of Central Tendency
14.5 The Mean
14.5.1 Calculation of Mean for Ungrouped Data
14.5.2 Calculation of Mean for Grouped Data
14.5.3 Calculation of Combined Mean
14.5.4 Use of Mean
14.5.5 Limitations of Mean
14.6 The Median
14.6.1 Calculation of Median for Ungrouped Data
14.6.2 Calculation of Median for Grouped Data
14.6.3 Use of Median
14.6.4 Limitations of Median
14.7 The Mode
14.7.1 Calculation of Mode for Ungrouped Data
14.7.2 Calculation of Mode for Grouped Data
14.7.3 Use of Mode
14.7.4 Limitations of Mode
14.8 Comparison of Mean, Median and Mode
14.9 Selection of an Appropriate Measure of Central Tendency
14.10 Let Us Sum Up
14.11 References and Suggested Readings
14.12 Answers to Check Your Progress
14.1 INTRODUCTION
As a teacher, we always deal with the data gathered from assessment of
student’s performance in continuous as well as terminal examinations. Many a
time, we get engaged with analyzing the data/score of the students and compare
them with other students or groups. We also prepare the progress report of
the students in which we use certain statistics to describe the performance of
the students in a meaningful and understandable way. We analyze the individual
score of the students as well as the group performance of the sections, classes
and schools. We also compare the performance of students between section
Analysing and Interpreting
Learner’s Performance
Keeping in view the above, the present Unit discusses the concept, process
and methods of calculation of measures of central tendency of the scores. In
the previous Unit, you have studied about the nature of data. In this Unit, you
will recapitulate the concept of individual and the group data. Further the Unit
will make you acquainted with various methods used for calculation of measures
of central tendency i.e. Mean, Median and Mode and also make you understand
the interpretation and use of the Mean, Median, and Mode. The Unit also makes
you acquainted with establishing relationships and comparisons among Mean,
Median and Mode.
14.2 OBJECTIVES
After going through this Unit, you will be able to:
differentiate between individual and group data;
explain the meaning of measures of central tendency;
compute mean from ungrouped and grouped data and interpret it;
compute and interpret the combined mean;
compute median from ungrouped and grouped data and interpret it;
compute mode from ungrouped and grouped data and interpret the it;
discuss the uses and limitations of mean, median and mode;
discuss the relationship of mean, median and mode;
compare the mean, median and mode for their relative importance in a
given context; and
select an appropriate measure of central tendency as per the nature of
data and purpose.
14.3 INDIVIDUALAND GROUPDATA
In the previous Unit, you have studied the nature of data, its organization, making
frequency distribution table and converting raw scores into group scores. To
recapitulate what you have studied earlier, we can say that the raw or the
individual score keeps very little meaning because it lacks value of interpreting
the score with other scores. At the same time, without knowing other individual
scores it is difficult to analyze the order and the position of an individual score
in the group. For example, let Sohan scored 50 in a test of Mathematics. What
does the score mean? How many students are below or above the score of
Sohan? Whether Sohan is an average, below average or above average student?
These questions can’t be answered simply from the individual score. To make
the individual score more meaningful, we can convert it into group scores. Group
scores can be presented in terms of average score, equal intervals, and also
ordering it both in ascending and descending order. Individual scores can be
presented as group score in terms of frequency distribution table. The individual
(raw score) and the group score have been presented in the following