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Welcome to class!
In today’s class, we will be talking about the measure of the central tendency of group data. Enjoy the class!
MEASURES OF CENTRAL TENDENCY
CONTENT
 MEAN
 MODE
 MEDIAN
They are the values which show the degree to which a given data or any given set of values will converge toward the central point of the data.
Measures of central tendency, also called measures of location, is the statistical information that gives the middle or centre or average of a set of data. Measures of central tendency include arithmetic mean, median and mode.
MEAN
This is the average of variables obtained in a study. It is the most common kind of average.
For group data the formula for calculating the mean is
$\frac{{\displaystyle \sum _{}^{}}fx}{{\displaystyle \sum _{}^{}}f}$
Where
$\sum _{}^{}$
=Summation
F=frequency
X=observation
MEDIAN
It is the middle number in any given distribution. The formula is
Median =
$L+\left(\frac{{\displaystyle \raisebox{1ex}{$N$}\!\left/ \!\raisebox{1ex}{$2$}\right.}\u2013Fb}{f}\right)c$
Where; L = Lower class limit.
N = Summation 0f the frequency.
Fb = Cumulative frequency before the median class.
f = frequency of the median class.
c= Class size.
MODE
It is the number that appears most in any given distribution, i.e the number with the greatest frequency. When a series has more than one mode, say two, it is said to be bimodal or trimodal for three.
Mode =
$L+\frac{D1}{D1+D2}$
Where M=mode
L = the lower class boundary of the modal class.
D1 = the frequency of the modal class minus the frequency of the class before the modal class.
D2 = the frequency of the modal class minus the frequency of the class after it.
C = the width of the modal class.
Example:
The table below shows the marks of students of JSS 3 mathematics.
Marks 
15  610  1115  1620  2125  2630 
Frequency  2  3  4  5  6  7 
Use the information above to calculate the following:
 the mean
 the median
 the mode
Solution
mark frequency midpoint fx
15  2  3  6 
610  3  8  24 
1115  4  13  52 
1620  5  18  90 
2125  6  23  138 
2630

7  28  196 
27 506
Mean=
$\frac{{\displaystyle \sum _{}}fx}{{\displaystyle \sum _{}}f}=\frac{506}{27}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}=18.7$
B. Median
Mark  F  Cf 
15  2  2 
610  3  5 
1115  4  9 
1620  5  14 
2125  6  20 
2630  7  27 
Median =
$\phantom{\rule{0ex}{0ex}}L1=15.5\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\raisebox{1ex}{$N$}\!\left/ \!\raisebox{1ex}{$2$}\right.=\raisebox{1ex}{$27$}\!\left/ \!\raisebox{1ex}{$2$}\right.=13.5\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}Fb=9\phantom{\rule{0ex}{0ex}}F=5\phantom{\rule{0ex}{0ex}}C=5\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}M=15.5+\frac{(13.5\u20139)\times 5}{5}\phantom{\rule{0ex}{0ex}}M=20$
$mode=L+\frac{D1}{D1+D2}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}L1=20.5\phantom{\rule{0ex}{0ex}}D1=7\u20136=1\phantom{\rule{0ex}{0ex}}D2=7\u20130=7\phantom{\rule{0ex}{0ex}}C=5\phantom{\rule{0ex}{0ex}}M=25.5+\left(\frac{1}{1+7}\right)\times 5\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}M=26.125$
General evaluation
The table below shows the weekly profit in naira from a minimarket.
You are required to calculate:
 The mean.
 The median.
 The mode.
Weekly profit(#)  110  1120  2130  3140  4150  5160 
Frequency  6  6  12  11  10  5 
Reading assignment
 Amplified and Simplified Economics for SSS by Femi Alonge page 2930.
 Further Mathematics Scholastics Series page 265265.
In our next class, we will be talking about the Measure of Dispersion of Variation of Grouped Data. We hope you enjoyed the class.
Should you have any further question, feel free to ask in the comment section below and trust us to respond as soon as possible.
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Please check the median and mode of the first table.