Chapter 3 - Numerical Descriptive Measures
Measures of Central Tendency for Ungrouped Data:
We often represent a data set by numerical summary measures, usually called the
typical values. A measure of central tendency gives the center of a histogram or a
frequency distribution curve. This section discusses three different measures of
central tendency: the mean, the median, and the mode.
The data that give information on each member of the population or sample
individually are called ungrouped data, whereas grouped data are presented in the
form of a frequency distribution table.
Mean
The mean, also called the arithmetic mean, is the most frequently used measure of
central tendency.
,Median
The median is the value of the middle term in a data set that has been ranked in increasing
order.
As is obvious from the definition of the median, it divides a ranked data set into two equal parts.
The calculation of the median consists of the following two steps:
1. Rank the data set in increasing order.
2. Find the middle term. The value of this term is the median. (1)
Note that if the number of observations in a data set is odd, then the median is given by the
value of the middle term in the ranked data. However, if the number of observations is even,
then the median is given by the average of the values of the two middle terms.
(1) The value of the middle term in a data set ranked in decreasing order will also give the
value of the median.
, Mode - represents the most common value in a data set.
The mode is the value that occurs with the highest frequency in a data set.
Measures of Central Tendency for Ungrouped Data:
We often represent a data set by numerical summary measures, usually called the
typical values. A measure of central tendency gives the center of a histogram or a
frequency distribution curve. This section discusses three different measures of
central tendency: the mean, the median, and the mode.
The data that give information on each member of the population or sample
individually are called ungrouped data, whereas grouped data are presented in the
form of a frequency distribution table.
Mean
The mean, also called the arithmetic mean, is the most frequently used measure of
central tendency.
,Median
The median is the value of the middle term in a data set that has been ranked in increasing
order.
As is obvious from the definition of the median, it divides a ranked data set into two equal parts.
The calculation of the median consists of the following two steps:
1. Rank the data set in increasing order.
2. Find the middle term. The value of this term is the median. (1)
Note that if the number of observations in a data set is odd, then the median is given by the
value of the middle term in the ranked data. However, if the number of observations is even,
then the median is given by the average of the values of the two middle terms.
(1) The value of the middle term in a data set ranked in decreasing order will also give the
value of the median.
, Mode - represents the most common value in a data set.
The mode is the value that occurs with the highest frequency in a data set.
