The document discusses measures of central tendency, which attempt to quantify the typical or average value in a data set. It gives the example of wanting to know the average gas mileage of a car or the typical salary for a particular job. The three main measures of central tendency discussed are the mean, median, and mode. It provides the formulas for calculating the mean or average for both population and sample data, and explains how to calculate it using Microsoft Excel. Quartiles and percentiles are also explained as ways to divide ordered data sets into parts to understand where values fall relative to others in the data.

2.  Measures of central tendency, or “location”, attempt to
quantify what we mean when we think of as the “typical”
or “average” score in a data set.The concept is extremely
important and we encounter it frequently in daily life. For
example, we often want to know before purchasing a car
its average distance per liter of petrol. Or before accepting
a job, you might want to know what a typical salary is for
people in that position so you will know whether or not
you are going to be paid what you are worth. Or, if you are
a smoker, you might often think about how many
cigarettes you smoke “on average” per day. Statistics
geared toward measuring central tendency all focus on
this concept of “typical” or “average”.

3. A.To get a single value the describes the
characteristics of the entire group.
It enables one to get a bird’s eye view of the entire
data. For example, it is impossible to remember the
individual scores of students in a test. But if the
average score obtained, we get a single value to
represent the entire group.
B.To facilitate comparison
By reducing the mass of data into one single figure,
comparison between 2 groups can easily be made.

4.  Simple arithmetic mean (or simply mean)
 The most common measure of central tendency and
is also average.
 Its value is obtained by adding together all the values
and dividing this total by the number of items
 The mean for a finite population with N elements is
denoted by µ (Greek letter mu)
 The mean for a sample of n elements is denoted by X
 Arithmetic mean may be categorized into simple
arithmetic mean and weighted arithmetic mean.

5.  Formula in getting the population mean
 µ=Exi/N
Where µ is the symbol for population mean
Exi is the sum of all the values of variable X
N is the number of observations
Formula in calculating the sample mean: X=Exi/n
Or X= x1+x2+x3+…Xn/n
Where X is the symbol for sample mean
Exi is the sum of all the values of variable X
N is the number of observations

6. 1. Add together all the values of the variable x
and obtain the total, i.e. Exi
2. Divide the total by the number of
observations, i.e N or n
Example: Calculate the average of the ff
population values:
3, 7, 5, 13, 20, 23, 39, 23,40
Solution: µ= Exi/N

7.  How to calculate the menu of ungrouped
data using MS excel
1. Open MS excel
2.Type or encode your data values in one
column
3. On a vacant cell, type =average(a1:a10)
4. Press Enter

8.  1. simple method
▪ Population Sample
Formula
µ= Exifi/N X= Exifi/N
µ is the population mean X is the sample mean
fi is the frequency fi is the frequency
xi is the midpoint of the class interval
N is the total frequency(population) (Sample)

10.  When a data set is arranged in ascending or
descending order, it can be divided not just in
2 parts but into various parts by different
values such as quartiles, deciles and
percentiles.These values are collectively
called quantiles or centiles and are the
extension of the median formula.

11.  Illustration
Lower Q Median Upper Q
Interpretation:
25% of all the data are less than or equal to Q1
50% of all the data are less than or equal to Q2 or median
75%of all the data are less than or equal to Q3
50% of all the data are lies between Q1 and Q3

12.  For un grouped data
3, 4, 5, 6, 6, 7, 8, 9, 9, 10 11
Find the lower and upper quartiles. Interpret the
answers.
Solutions:
Since there are 11 values, the 3rd item is Q1=5, the
middle item is Q2=7 and the 9th item is Q3=9
Now what does this mean?

13.  ¼ or 25% of the data has a value that is less
than or equal to 5
 ½ or 50% of the data has a value that is less
than or equal to 7
 ¾ or 75% of the data has a value that is less
than or equal 9 and
 ½ or 50% of the data lies between 5 and 9

14.  A decile is any of the nine values that divide
the sorted data into ten equal parts, so that
each part represents 1/10 of the sample or
population.
 Deca means ten.

15. D1 D2 D3 D4 D5 D6 D7 D8 D9 100%
D1 is denoted as the 1st decile under which 10% of the
total population lies.
D2 is denoted as the second decile under which 20% of
the total population lies.
D3 is denoted as the third decile under which 30% of the
total population lies.

16.  D1=P10;D2=P20;D3=P30 and so on. For every
one decile you multiply 10 to get the
percentile.
 The 25th percentile is also known as the 1st
quartile(Q1), the 50th percentile as the
median or 2nd Quartile (Q2) and the 75th
percentile as the 3rd Quartile (Q3)

17.  A percentile is any of the 99 values which divide
an ordered data set into 100 equal parts so that
each part represents 1/100 of the data set.The
word “percentile” comes from the latin word
per centum which means “per hundred”.
 Percentiles are generally used for large sets of data.
 Sometimes low percentile=good and
high percentile = good, depending on the
context.

18.  70th percentile for a test was 16/20. what does
this mean?
 Answer:
 Analysis: 1/20; 2/20; 5/20; 6/20; 11/20;
13/20;16/20;17/20
Smallest to Largest percentile
70% got 16/20 or less in the test
30% got more than 16/20
Here a high percentile would be considered good
since answering more questions correctly is
desirable

19.  Runners in a race want to finish in a time that is
less than anyone else.
low percentile is better- want a fewer people to
have that is less than yours
suppose the 20th percentile is 5.2 minutes.This
means that 20% of the people had a time that
was quicker or less than 5.2 minutes. 80% of the
people hat a time that was slower or more than
5.2 minutes.Thus, 5.2 minutes is considered as
good.

20.  Mary, a teacher, receives a salary that falls in
the 78% percentile.
This means that 78% of teachers has a salary
that is less than or equal to hers.
25%? Of the teachers has a salary that is more
than hers. Mary should be pleased with this
fact.