Mathematics Assignment: Fractions, Decimals, and Statistics

This assignment provides a comprehensive solution to a mathematics homework covering various topics. Part 1 focuses on fundamental concepts like numerators, denominators, fraction simplification, and percentage calculations. It includes practical problems involving money, significant figures, and discounts. Part 2 analyzes Olympic medal data, requiring the interpretation of tables, identification of trends, and comparison of countries based on medal counts. Part 3 delves into Excel applications, instructing on ranking teams, using conditional statements, creating bar charts, and calculating sums. It also covers advanced functions such as SUMIF, MATCH, and IF, along with the calculation of median, mean, and standard deviation. The assignment also covers the use of Excel for data representation and interpretation.

MATHS

TABLE OF CONTENTS
PART 1............................................................................................................................................3
PART 2............................................................................................................................................5
PART 3............................................................................................................................................7
REFERENCES..............................................................................................................................14

PART 1
1. Numerator: When any number is written in the form of a fraction, it is represented as a/b
where a is the numerator which means the top part in fraction is numerator. It represents
part of whole (Liu, Gai and Zhou, 2016).
Denominator: The bottom part of a fraction is denominator which represents the
complete whole.
For example, in a fraction 2/5, 2 is the numerator and 5 is the denominator.
2. 24/40 can be expressed as 3/5 in its simplest form as it can be reduced as:
24/40= 12/20=6/10=3/5
And, 18/42 can be written as 3/7 as it can be reduced as:
18/42=9/21=3/7
3. a. 2/3*4/4= 8/12
3/4*3/3=9/12
5/6*2/2=10/12
b. Total number of books in the library= 60,000
Books of business= 14,000
Books on healthcare=22,000
Books on psychology and law=12,000
Remaining books= 60,000-14,000+22,000+12,000=12,000
Books on computing= 2/3 * 12,000=8000
Percentage of Computing books= 8,000/60,000*100=13.33%
4. Money Liz has given to sales attendant= 3*£50= £150
Money Liz got in return=£10.50
Cost of two pair of shoes= £150-£10.50= £139.5
Price of each pair of running shoes= £139.5/2= £69.75
5. a. 240.50 x 19.54= 4699.37
Answer up to 2 significant figures= 47
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b. 52100=5.21*104
6. a. Total discount offered by gym= 30%
Total amount given by Patty and her two siblings= £210
Let the total amount paid by 3 of them before discount be x.
Total amount before discount can be calculated as:
x-(30/100*x) = £210
x= £300
Total savings= £300-£210=£90
b. Average savings per person= Total Savings/3
= £90/3= £30
7. a. 3/4-7/9+2/3= 3/4-(7/9+2/3) (Applying BODMAS)( Kuksin, 2018)
= 3/4- {(7+8)/9}
=3/4- 13/9
= (27-52)/36
= -25/36
b. The largest number among 0.1, 0.02, 0.003, 0.0004, 0.00005 is 0.1 as it 1 part of 10.
0.1=1/10, 0.02=2/100, 0.003=3/1000, 0.0004=4/10000, 0.00005=5/100000 which
means 1/10 is the largest number making 0.1 the largest among all.
8. Total no. of men who were asked= 90
Total no. of women who were asked= 60
Total no. of people who were asked= 150
Total number of people said yes= 3/5*150= 90
Total number of women said yes= 3/10*60= 18
Total no. of men said yes= 90-18= 72
Total no. of men said no= 90-72=18
Total percentage of men said no= 18/90*100= 20%
9. Annabelle can leave home at 8.05 am. The working is as shown below:
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Home Euston Rail station Birmingham Meeting Venue
If Annabelle leaves home at 8.05 am, she will reach Euston Rail station at 9.05 am from
there she can get the train 5 minutes past the hour and can reach Birmingham at 10.15
am. From there in 5 minutes she can easily reach the meeting venue at 10.20 and can get
ready for the meeting at 10.30.
10. Weight of box of Shredded wheat= 0.35 kg =35/100 kg
Weight of box of Weetabix wheat=9/25 kg=0.36=36/100 kg
This means that 0.36 i.e., 9/25 is much greater than 0.35.
Therefore, box of Weetabix wheat is much heavier than box of Shredded one.
PART 2
11. a. The country Hungary had the lowest number of overall medals i.e., 491 among ten
countries.
b. Soviet Union and China competed in the least i.e., 10 number of games.
c. The mode in the number of games is 27 as it is repeated maximum number of times in
Italy, Sweden and US.
d. Range (in gold medals) = Highest value- Lowest Value
= 1,022-147
=875
e. 4 countries i.e., China, Great Britain, Soviet Union and United States got more silver
medals than bronze medals.
Team Gold Silver
China 165 151
Great Britain 295 289
Soviet Union 357 325
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United States 794 704
f. Germany and Soviet Union got more gold medals, more silver medals and more bronze
medals than Great Britain.
g. Soviet Union did the best as the ratio of total number of medals to the number of
games is highest in this country as compared to others i.e., 1122:10= 112.2:1
h. The TWO likely reasons which does not feature Jamaica in the top 10 medals are as
follows:
 The one reason is that Jamaica’s players did not win the medals in other sports
except athletics and the top 10 countries promoted many games rather than
focusing on one and in athletics also the number of medals were very less as
compared to the one which are featured in top 10.
 The another reason is that the other games like Basketball, Football and many
others which were played in Jamaica did not represent it at the Olympics or
internationally.
i. As given in the table, the closest competitor of US in terms of total no. of medals is
Soviet Union i.e., 2,520 in US and 1122 in Soviet Unions.
Among all the three medals Gold, Silver and Bronze,
The difference between the number of gold medals in both the countries is 1,022-440=582
The difference between the number of silver medals in both the countries is 794-357=437
The difference between the number of bronze medals in both the countries is704-325=379
Therefore, in the Bronze category, US outperformed its closest competitor Soviet Union.
j. Australia, Germany and Hungary had the most evenly distributed number of gold,
silver and bronze medals.
Australia: 147, 163, 187
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Germany: 275, 313, 349
Hungary: 175, 147, 169
PART 3
a. In order to rank the teams from 1 to 10, the RANK function can be applied as follows:
 Make a column named rank.
 Enter the formula of rank in the first cell of rank column,
=RANK(B2,$B$2:$B$11) (Yasun and Daud, 2020)
 Copy the formula from the cell C2 down to last data cell, and the scores are
ranked.
b. In order to display the Teams whose total no. of medals is greater than or equal to 800,
then the condition if can be used in the spreadsheet as:
 Click on the sell and write the Formula
=IF(F2>=800,” TRUE”)
 Click on enter.
 The above function will print true if the condition becomes true and it will print
false if it does not follow the condition.
 Using this, one can segregate the entries according to various conditions.
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c. Bar chart can be used to display only the details of the gold medals of different teams.
d. Replication can be checked using the bar chart or any other chart. Chart is made for the
column to be checked for replication and by observing the graph, it can be checked that
whether the column contains replicated data or not. Here, through the following graph,
replication in column of Total number of games was checked. The result was obtained
that 10, 26, 28 occurred 2 times each and 27 occurred 3 times which means that
replication was there in column of number of games.
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e. Sum of the values can be calculated by using the function SUM as follows:
At the end of the column, after all the entries, the formula of SUM is written as
=SUM (First number, last number) and then click enter. Sum of all the values of the
respective column will be displayed (Held, Moriarty and Richardson, 2019).
14. a. In order to obtain the total number of medals for Germany and Great Britain, the
formula will be used as
=SUM (F5:F6)
Where F is the column of total medals and 5 is the row of Germany and 6 is the row of Great
Britain.
b. The European countries among all the mentioned 10 countries are France, Germany,
Hungary and Italy. The average number of silver medals can be calculated by using the formula
mentioned below:
=average (D4:D5:D7:D8)
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Where D is the column of silver medals and 4, 5, 7 and 8 represents the four European
countries.
c. SUMIF (B2:B11,” <” &20, C2:C11)
The above function will add the values of the gold medals of the team who has number of
games less than 20.
d. MATCH (Italy, A2: A11,0)
The above function matches the value of Italy in the cell range A2 to A11 and 0 the match type
denotes that it is an exact match.
The Total medals can be shown by the IF function as:
if (B2:B11, Italy, F2:F11)
here, B2:B11 is the range of team and F2:F11 is the total number of medals.
15. a. The median of Gold medals is 219.5.
The median of Silver medals is 209.5.
The median of Bronze medals is 226.5.
The formula for determining median for the gold medals is =MEDIAN (C2:C11)
b. The mean number of Gold medals is 311.4
The mean number of Silver medals is 282.3
The mean number of Bronze medals is 280.6
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The formula for calculating the mean number =AVERAGE (E2:E11)
c. The standard deviation can be calculated as follows:
For Australia, S.D.= [1/3{(147-165.66)2+(163-165.66)2+(187-165.66)2}]1/2
=16.43844
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d. After going through the spreadsheet above, it is basically a measure of spread of data set away
from mean of data (Kapoor and et.al.,2018). It can be interpreted easily by the use of Standard
Deviation that whether the data is close to the average or not (Bishop and et.al.,2017). It helped
in comparing the data sets easily and also to find which data set is close to the average and which
is not.
16. a. Comparison of total no. of medals won by various countries.
b. Graph showing the contribution of each country to the total medals.
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REFERENCES
Books and Journals
Bishop, S.A. and et.al.,2017. Survey datasets on the externalizing behaviors of primary school
pupils and secondary school students in some selected schools in Ogun State,
Nigeria. Data in brief. 13. pp.469-479.
Held, B., Moriarty, B. and Richardson, T., 2019. Microsoft Excel Functions and Formulas.
Stylus Publishing, LLC.
Kapoor, R. and et.al.,2018. Boosting performance of power quality event identification with KL
Divergence measure and standard deviation. Measurement. 126. pp.134-142.
Kuksin, S., 2018. Asymptotic properties of integrals of quotients, when the numerator oscillates
and denominator degenerates. arXiv preprint arXiv:1803.06694.
Liu, X.L., Gai, S.S. and Zhou, J., 2016. Journal impact factor: do the numerator and denominator
need correction?. Plos one. 11(3). p.e0151414.
Yasun, A.S. and Daud, S.A., 2020. Using some of Microsoft Office Excel Functions to Compute
Soil Engineering Parameters Based on Raw Results of Laboratory Tests. In Key
Engineering Materials (Vol. 857, pp. 273-282). Trans Tech Publications Ltd.
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