PAPER
STATISTICS ( MEAN,MEDIAN, AND MODE )
ENGLISH FOR MATHEMATICS
ARRANGED BY :
ADINDA AULIA LATIFAH
19029065
Lecturer : Dra.Hj.Fitrani Dwina,M.Ed.
UNIVERSITAS NEGERI PADANG
FACULTY OF MATH AND SCIENCE
MAJORING IN MATHEMATICS EDUCATION
2020
PREFACE
By extending gratitude to the presence of Allah SWT and with the grace, i can make
this paper as my task. As learning material, i hope it can be received and uderstood together.
This paper is about STATISTICS ( MEAN,MEDIAN,AND MODE). This paper was
submitted to fulfilll the task of English for Math.
I would like to say thank you to Mrs. Hj. Dra. Fitrani Dwina, M.ed, as a lecturer in
English for Math who has given this assignment so that i can add to my knowledge and
insight in accordance with the field of study that I'm going through now.
This paper might still not be perfect,therefore i expect constructive criticism and
suggestions for the perfection of this paper. Finally, i humbly apologize if something goes
wrong in asking for or deciphering my paper. Hopefully,it can be received by ma’am and can
be used as a referency in my learning process.
Padang,
March 2020
Adinda Aulia Latifah
CHAPTER I
PRELIMINARY
A. ISSUE BACKGROUND
In everyday life,every thing has data. Be it recorded or not. In some cases data
collection is needed for existing data. In statistical learning. We can collect a data. There are
several parts to collecting data,but there are three that are often used, the mean,median,and
mode.
We know that statistics deals with data collected for specific purposes. We can make
decisions about the data by analysing and interpreting it. Mean,median,and mode is the part
of statistics. So many part of statistics,but i think this are the three most commonly used in
obtaining data. The data is divided into two,namely single data and group data . the
mean,median,and mode can be used in single data or group data.
B. PROBLEM IDENTIFICATION
1. The mean on a single data
2. The median on a single data
3. The mode on a single data
4. The mean on a group data
5. The median on a group data
6.
The mode on a group data
C. AIMS
1. Know the mean on a single data
2. Know the median on a single data
3. Know the mode on a single data
4. Know the mean on a group data
5. Know the median on a group data
6. Know the mode on a group data
CHAPTER II
DISCUSSION
1. The mean
The mean is a data callection technique that is based on the average value of a data.
This is can be obtained by the sum of all data divided by a lot of data.
a. The formula of the mean on a single data
𝑥̅ =
𝑥1 + 𝑥2 + ⋯ + 𝑥𝑛
𝑛
or
𝑛
1
𝑥̅ = ∑ 𝑥𝑖
𝑛
𝑖=1
b. The formula of the mean on a group data
𝑛
1
𝑥̅ = ∑ 𝑓𝑖 𝑥𝑖
𝑛
𝑖=1
Information :
𝑥̅ = the mean
n = the sum of all frequencies
𝑥1 = the first data
𝑥2 = the second data
𝑥𝑛 = 𝑛𝑡ℎ 𝑑𝑎𝑡𝑎
𝑥𝑖 = midpoint of i-class
𝑓𝑖 = frequency of i-class
2. The median
Median is the middle value of data that has been sorted from the smallest value. If the
odd data,then the median of the data is the value in the middle. While if the even data,then
the median is the average of the two value in the middle.
a. The formula of the median (even data) on a single data
Me =
𝑥𝑚 +𝑥𝑛
2
b. The formula of the median on group data
𝑛
− (∑ 𝑓)2
𝑀𝑒 = 𝐿2 + (2
)𝑐
𝑓2
Information :
Me = the median
𝑥𝑚 = one of the values in the middle
𝑥𝑛 = one of the values in the middle
𝐿2 = the lower edge of the median class
n = the sum of all frequencies
f = the number of frequencies before the median class number
𝑓2 = the frequency of the median class.
c = the length of the interval class.
3. The mode
Mode is a value that often appears in a data. Modus can have more than 1. If you find
the value with the largest frequency there is 2, the mode is the two values. Mode is used to
find out the frequency of occurrence of an event. Mode can be used for all measure ment
scales of data ranging from nominal to ratio.
The formula of the median on group data
𝑑1
𝑀𝑜 = 𝐿0 + (
)𝑐
𝑑1 + 𝑑2
Information :
Mo = the mode
𝐿0 = lower limit of interval class with the mosy frequency
𝑑1 = class mode frequency minus the frequency of the previous class
𝑑2 = mode class frequency minus class frequency afterwards
c = length of interval class
Example :
1. Consider the following data :
a. 4 8 5 6 2 3 9 5 3
b. 2 9 3 2 4 4 8 7 2 9
Determine the mean,median,and mode !
a. The mean
𝑥̅ =
𝑥̅ =
𝑥1 + 𝑥2 + ⋯ + 𝑥𝑛
𝑛
4+8+5+6+2+3+9+5+3
9
𝑥̅ =
45
9
𝑥̅ = 5
The median
233455689
So, Me = 5
The mode
Mo = 3 and 5 ( because this are value appears the most,which is 2 times for each
value ).
b. The mean
𝑥̅ =
𝑥̅ =
𝑥1 + 𝑥2 + ⋯ + 𝑥𝑛
𝑛
2+9+3+2+4+4+8+7+2+9
10
50
𝑥̅ =
10
𝑥̅ = 5
The median
2223447899
Me =
𝑥𝑚 +𝑥𝑛
2
Me =
4+4
2
Me = 4
The mode
mo = 2 because this are value appears the most,which is 3 times for each value.
2. given grouped data as below.
Interval class
frequency
1-5
6-10
11-15
16-20
21-25
Determine the mean,median, and mode !
6
4
2
3
1
a. The mean
Determine the midpoint of each class with this formula.
𝑥𝑖 =
We can get,
𝑥1 =
5,5 + 0,5
=3
2
𝑥2 =
10,5 + 5,5
=8
2
𝑥3 =
15,5 + 10,5
= 13
2
𝑥4 =
20,5 + 15,5
= 18
2
𝑥5 =
25,5 + 20,5
= 23
2
𝑇𝑎 + 𝑇𝑏
2
Value
Frequency
𝒙𝒊
𝒇𝒊 𝒙𝒊
1-5
6-10
11-15
16-20
21-25
Total
6
4
2
3
1
16
3
8
13
18
23
total
18
32
26
54
23
153
𝑥̅ =
∑ 𝑥𝑖 𝑓𝑖
∑ 𝑓𝑖
𝑥̅ =
153
16
𝑥̅ = 9.5625
b. The median
Value
1-5
(mode)
6-10
(median)
11-15
16-20
21-25
Frequency
6
𝒇
6
4
10
2
3
1
12
15
16
𝑛
− (∑ 𝑓)2
𝑀𝑒 = 𝐿2 + (2
)𝑐
𝑓2
16
−6
𝑀𝑒 = 5.5 + ( 2
)5
4
8−6
𝑀𝑒 = 5.5 + (
)5
8
2
𝑀𝑒 = 5.5 + ( ) 5
8
𝑀𝑒 = 5.5 + 1.25
𝑀𝑒 = 6.75
c. The mode
𝑑1
𝑀𝑜 = 𝐿0 + (
)𝑐
𝑑1 + 𝑑2
6
𝑀𝑜 = 0.5 + (
)5
6+2
6
𝑀𝑜 = 0.5 + ( ) 5
8
𝑀𝑜 = 0.5 + 3.75
𝑀𝑜 = 4.25
CHAPTER III
FINAL
A. CONCLUSION
1. Single data is a data that is estimated to be less than 30 and doesn’t require tables.
Whereas group data is a data more than 30 and a table is needed to group them.
2. The mean is a data callection technique that is based on the average value of a data.
3. The mean is a data callection technique that is based on the average value of a data.
4. Mode is a value that often appears in a data.
B. SUGGESTIONS
This paper may still be not perfect. Therefore,critics and suggestions are needed to
perfect this paper. It is also hoped that this paper can be used to increase our knowledge.
REFERENCE
NCERT.2017.Mathematics:textbook for class XI.India:National Council of Educational
Research and Training.
HTTP://DE.WIKIBOOKS.ORG/WIKI/BENUTZER:DIRK_HUENNIGER/WB2PDF.
ENCLOSURE