Using Numeracy, Data & IT
Portfolio of Tasks
Part One
Question 1
a) A percentage analysis brings comparison between one quantity against the other quantity
of similar relationship rebased to 100.The percentage term is derived from the per 100
concept. It is represented by the symbol “%”. Therefore, one quantity is expressed to
another quantity per 100. %. (Croft and Davison 2016). Examples of percentages include
30%,0.125%,75%.
b) A ratio is an expression which compares two similar quantities by division. The concept
applies to quantities of same kind. Ratio uses the symbol “:” or division “/” sign to bring
comparison (Nash et al 2012). The two expressions can either be represented as; Quantity
one: Quantity two or Quantity one/Quantity two. Quantity one is referred to as antecedent
while quantity two as consequent (Nash et al 2012). Examples of ratios include
2:3,2kgs:5kgs,3/9.
Question 2
a
12
20
to its simplest form
=
b.
3
5
36 ∶ 72 in its simplest form
=1∶2
c.
Equivalent fractions with a denominator of 20 of;
4
3
4
2
5
d.
7
9
8
is
10
is
is
20
15
20
8
20
3
2
28 + 27+24
4
3
36
+ + =
79
7
=2
36
36
e.
Mean =
∑n
i=1 x
n
=
301 + 285 + 20 + 351 + 35 + 205 + 311 + 25 + 45 + 310 + 301 + 305
12
=
2,494
= 207.8333
12
= 207.83 (2 d. p)
Question 3
(Neil and Johnson 2018)
a. Total staff members on the organisation = 80,000
sales team = 16,000 Customer support team = 24,000
Software development and HR team = 14,000
Remainig staf = Total staffs − {sales team + Support + HR team}
Remaining Staff = 80,000 − {16,000 + 14,000 + 24,000}
= 80,000 − 54,000 = 26,000 members
Finance team =
2
of the remaining staff.
5
2
= 5 of 26,000 = 10,400 members
% Finance staffs =
=
Finance Staff
× 100
Total Staff
10,400
× 100 = 13%
80,000
b. Software development and HR team = 14,000
total Ticket payments = 3 × £25
= £75
balance = £10.5
tickets expenses = £75 − £10.5 = £64.5
total legs of the journey = 2
one leg of the journey =
£64.5
= £32.25
2
c.
Given the Meeting starts at 10:45 am.
Working backwards.
If Rail journey from Euston to Birmingham = 1 hour 10 minutes
Time from Birmingham to the meeting venue = 5 minutes
Therefore, latest arrival time at Birmingham = 10: 30 am − 5 minutes
= 10: 25 am
Latest departure time of train from Euston to Birmingham
= 10: 25 am − 1 hr 10 minutes
= 9: 15 am
Take note that the past hour time therefore, will be 9:00 am.
Given the Train to Birmingham running times are;
5 minutes past hour,25 minutes past hour and 45 minutes past hour.
Therefore, the possible times to board the train are;
9: 00 am + 5 minutes = 9: 05 a. m.
and arrival at the venue
= 9: 05 am + 1 hr 15 minutes
10: 20 which is 10 minutes early
9.00am + 25 mins = 9: 25 a. m
and arrival at the venue
9: 25 am + 1 hr 15 minutes
= 10: 40am which is 10 minutes late
9.00 am + 45 minutes = 9: 45 a. m
and arrival at the venue at
= 9: 45 am + 1 hr 15 minutes = 11: 00 which is 30 minutes late
Given Time taken to from Home to Euston is 1 hour.
The possible latest time that she leaves home to meet the train running times of 5
minutes, 25minutes and 45 minutes past the 9.00 a.m. hour will be;
9: 00am − 1 hour = 8: 00 am therefore the latest time she will leave to board the
9.05 trains is 8:05a.m.
where she will arrive at interview 5 mins early and hence prepare.
d.
men = 15, women = 75
Total people = 15 + 75 = 90 people
those who sad yes in the survey =
men who said yes =
2
of 90 = 36 people
5
6
of 15 = 6
15
men men who said no = 15 − 6 = 9
total of people who said no = 90 − 36 = 54
women who said no = people who said no − men who said no
= 54 − 9 = 45
percentage of women who said no out of the total survey =
= 50%
45
× 100
90
Question 4.
(Croft and Davison 2016)
a. work rate = £240 per hour
work time = 19.5 hours
earned money = work rate × work time
= £240 per hour × 19.5 hours
= £4,680
c.
utilities and savings in a ratio of 2: 3
utilities =
2
of the earnings
5
allocation to her savings =
3
of earnings
5
earnings = £4,680
=
3
× £4,680 = £2,808
5
Question 5.
(Croft and Davison 2016)
a. vacant beds = 30% ,total beds = 100%
occupied beds = 70% ,current patients = 210
occupied beds = cuurent patients
therefore, if 30% = 210,
100% = total beds
=
100% × 210
= 700 beds
30%
b. Increase bed capacity by 15%
Initial bed capacity =100%
New bad capacity=100%+15%=115%
new bed capacity
Planned bed capacity =initial bed capacity × 100
=
115%
× 700 = 805 beds
100%
c. paracetamol weight = 0.55 kgs
Ibuprofen weight =
14
kg
25
convert their weights to percentage by multiplying by 100
paracetamol weight = 0.55 kgs × 100 = 55%
Ibuprofen weight =
14
kg × 100 = 56%
25
therefore , ibuprofen has the greatest weight because
it has a higher percentage of 56% compared to paracetamol with 55%.
Part 2: People and Society Pathway.
Question 6
a. Year 2020 with 67,352.
b. Year 2019 with 9,145
c. The median UK population between 2016 and 2020
65,648,100
66,040,200 66,435,600 66,796,800 67,081,000
78,740 81,904 81,943 83,604 84,441
The median represents the middle value of the data arranged in ascending order
(Croft and Davison 2016)
National UK population Median = 66,435,600
UK prison population median =81,943
d. Range =Maximum value – Minimum value
Maximum number remanded =11,388
Minimum number remanded =9,145
Range =11,388 -9,145=2,243
e.
Year
Number of
Number of non-
sentenced
criminal
Ratio
𝑆𝑒𝑛𝑡𝑒𝑛𝑐𝑒𝑑 𝑝𝑟𝑖𝑠𝑜𝑛𝑒𝑟𝑠
𝑛𝑜𝑛−𝑐𝑟𝑖𝑚𝑖𝑛𝑎𝑙 𝑝𝑟𝑖𝑠𝑜𝑛𝑒𝑟𝑠
prisoners each
prisoners.
year
2016
74,316
1,530
74,316
2017
74,803
1,422
74,803
2018
72,619
869
72,619
2019
72,798
769
72.798
2020
67,352
774
67,352
The years include 2018, 2019 and 2020.
1,530
1,422
869
769
774
=48.57
Below sixty times
=52.60
Below sixty times
=83.56
Above sixty times
=94.67
Above sixty times
=87.01
Above sixty times
f.
Years
Total
Total national
Prison per capita
% Prison per capita (% in
population of
population of UK
𝑇𝑜𝑡𝑎𝑙 𝑈𝐾 𝑃𝑟𝑖𝑠𝑜𝑛𝑒𝑟𝑠 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛
𝑁𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝑈𝐾 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛
𝑇𝑜𝑡𝑎𝑙 𝑈𝐾 𝑃𝑟𝑖𝑠𝑜𝑛𝑒𝑟𝑠 𝑝𝑜𝑝
𝑁𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝑈𝐾 𝑝𝑜𝑝𝑢𝑙𝑎
UK prisoners
2016
83,604
65,648,100
2017
84,441
66,040,200
2018
81,904
66,435,600
2019
81,943
66,796,800
2020
78,740
67,081,000
83,604
65,648,100
84,441
66,040,200
81,904
66,435,600
81,943
66,796,800
78,740
67,081,000
= 0.001273517
0.1274%
= 0.00127863
0.1279%
= 0.001232832
0.1233%
= 0.00122675
0.1227%
= 0.000811075
0.0811%
The results in the table above shows that 2017 had the greatest number of prison
per capita of 0.1279% compared to 0.1274% ,0.1233%,0.1227% and 0.0811% in
that order.
g. 2016 the country registered a higher population of prisoners compared to 2020
this showed a drop in the prison population. This can be justified by prisons
reforms and human right considerations that Number of sentenced prisoners each
year and alternatives to imprisonment that may have been introduced that year.
Another reason to justify the drop of population of prisoners in the year 2020 may
have been due to the lockdown measures introduced in the country in response to
the Covid-19 pandemic that was experienced in the end of the year 2019 when a
first case was confirmed. The move was to cub the contagious disease from
spreading.
Question 7.
a.
b.
Step 1-Highlight the table and consider sort and filter icons.
Step 2-Open a data tab by right clicking the mouse once in the spreadsheet. And click on
the Sort and drop list.
Step 3-Sort the values in the column to an increasing order, which is alphabetically
represented from A to Z
(Nash et al 2012)
c. Select a single blank cell from the UK prison population column.
Type
=MAX(IF(F4:F7<66700000,F3:F7)) in the blank cell. Drag in the column to
determine F4:F7, this represents the range of values of the total population.
Type the less the symbol “<66700000” then ‘,” then drag the values in the column.
The final syntax will look like this. =MAX(IF(F4:F7<66700000,F3:F7))
Finally, press the Shift + Ctrl + Enter keys on the keyboard simultaneously.
(Nash et al 2012)
d.
A bar chart.
e. Column F
f.
From 2016-2020 total number of recorded non-criminal prisoners is their sums using excel
the following formulae is used.
=SUM(E3:E7)
= 6,023
Question 8
a. A Scatter Plot or a line graph.
b.
UK Prison Population
National
Total UK Prison
Population
Population
65648100
83,604
66040200
84,441
66435600
81904
66796800
81943
67081000
78740
85 000
Correlation between National Population to Prison
Population in UK
Prison Population
84 000
83 000
82 000
81 000
80 000
79 000
78 000
65400000 65600000 65800000 66000000 66200000 66400000 66600000 66800000 67000000 67200000
National Population
c. Negative Correlation.
Question 9
a. Median of each custody is determined by arranging the population in each custody in
ascending or descending order the picking the middle value (Nash et al 2012).
Number remanded:11388 ,9638 ,9288 ,9285 ,9145 median = 9288
Number Sentenced :74803 ,74316 ,72798 ,72619 ,67352 Median =72798
Number of Non-Criminal Prisoners:1530 ,1422 ,869, 774, 767 Median =869
b. The average of each custody is determined by taking the totals of each custody then
dividing it by the total number of years (Croft and Davison 2016).
Average of number sentenced =
𝑡𝑜𝑡𝑎𝑙𝑠 𝑜𝑓 𝑛𝑢𝑚𝑏𝑒𝑟 𝑠𝑒𝑛𝑡𝑒𝑛𝑐𝑒𝑑
𝑡𝑜𝑡𝑎𝑙 𝑦𝑒𝑎𝑟𝑠
74316 + 74803 + 72619 + 72798 + 67352
= 72,177.6
5
= 72,177
Average of non-criminal’s prisoners =
𝑡𝑜𝑡𝑎𝑙𝑠 𝑜𝑓 𝑛𝑜𝑛−𝑐𝑟𝑚𝑖𝑛𝑖𝑎𝑙 𝑝𝑟𝑖𝑠𝑜𝑛𝑒𝑟𝑠
𝑡𝑜𝑡𝑎𝑙 𝑦𝑒𝑎𝑟𝑠
1530 + 1422 + 869 + 774 + 767
= 1072.4
5
= 1072
Mean of number remanded =
𝑡𝑜𝑡𝑎𝑙𝑠 𝑜𝑓 𝑛𝑢𝑚𝑏𝑒𝑟 𝑟𝑒𝑚𝑎𝑛𝑑𝑒𝑑
𝑡𝑜𝑡𝑎𝑙 𝑦𝑒𝑎𝑟𝑠
11388 + 9638 + 9288 + 9285 + 9145
= 9748.8
5
= 9748
c. Standard deviation of column F by excel is shown on the spreadsheet below.
UK Prison Population(2016-2020)
Year
National
Population
Number
Number
Remanded
sentenced
Number of
Total UK
Non-Criminal
Prison
Prisoners
Population
2016
65648100
9,288
74,316
1,530
83,604
2017
66040200
9,638
74,803
1,422
84,441
2018
66435600
9,285
72,619
869
81904
2019
66796800
9,145
72,798
767
81943
2020
67081000
11,388
67,352
774
78740
934.2476652
2963.596852
372.592673
2184.689749
STDEV
STDEV.P
1954.045916
d. The Standard Deviation measures the extent of a set of values varies or deviates from
their corresponding averages preferably referred as the data mean (Neil and Johnson
2018). The standard deviations specifically rely on the dataset whether the data represents
a fraction of the whole data called sample or the whole entire dataset known as
population (Neil and Johnson 2018).
Standard deviation is computed after deviations of the data are obtained from the mean of
the data values. The mean is the average of the data, where a sum of all the values is
divided by the total number of values in the dataset (Nash et al 2012). The resultant is
then squared and their total summations recorded. The squared deviations depict the
variation or variance of the data sets (Neil and Johnson 2018).
The Standard deviations is very essential as a measure of dispersion because its value is
always fixed and well defined as is based on all the observations in series. Additionally, it
is applied in other statistical techniques like correlation and regression analysis (Nash et
al 2012)
Despite its usefulness, standard deviations face demerits it cannot be used for comparing
the dispersion of two or more series of observations given different units and too gives
more weight to extreme values. (Neil and Johnson 2018)
Question 10.
a. =SUMIF(C3:C7,">9150",F3:F7)
=328689
b. =AVERAGEIF(E3:E7,">1000",F3:F7)
=84022.5
c. =SUMIF(C53:C57,"<9150",F53:F57)
d. =VLOOKUP(A6,A3:F7,1,FALSE)
=2019
=VLOOKUP(F6,A3:F7,6,FALSE)
=81943
UK Prison Population(2016-2020)
Year
National
Population
Number
Number
Remanded
sentenced
Number of Non-
Total UK Prison
Criminal Prisoners
Population
2016
65648100
9,288
74,316
1,530
83,604
2017
66040200
9,638
74,803
1,422
84,441
2018
66435600
9,285
72,619
869
81904
2019
66796800
9,145
72,798
767
81943
2020
67081000
11,388
67,352
774
78740
328689
84022.5
2019
81943
Question 11
a. The Combined bar graph produced assist to bring comparison among the numbers of
prisoners in each custody type between the year 2016 to 2020.
Number of Non-
Year
Criminal Prisoners
Number
Number
Remanded
sentenced
2016
1,530
9,288
74,316
2017
1,422
9,638
74,803
2018
869
9,285
72,619
2019
767
9,145
72,798
2020
774
11,388
67,352
A Combine Bar Chart
80 000
74 803
74 316
72 798
72 619
67 352
70 000
Prisoners Custody
60 000
50 000
40 000
30 000
20 000
10 000
9 288
1 530
9 638
1 422
9 285
869
9 145
11 388
774
767
0
2016
2017
2018
2019
Years
Non-Criminals
Remanded
Sentenced
2020
b. A combined bar chart produced above gives a glimpse of comparison among three
custodies. One can easily see the trends in every custody. The observation shows an
increase in the number of remanded prisoners and decrease in the numbers of noncriminal prisoners and the number of those sentenced.an increase in the population of
those being remanded and the non-criminal can be justified by high bail rates or denials
by the law courts. The decrease trends in those sentenced may be affected by the change
in prisoners’ rights and reforms imposed by the government and human rights
organizations.
(Neil and Johnson 2018)
c.
PIE CHART
Shows proportions of prison custodiese of 2019
Remanded
Non-Criminal, [], []
Sentenced, [], []
𝑛𝑢𝑚𝑏𝑒𝑟 𝑟𝑒𝑚𝑎𝑛𝑑𝑒𝑑
Percentage of number remanded to total Prison population = 𝑃𝑟𝑖𝑠𝑜𝑛 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 ×
9145
100 = 81943 × 100 = 11.16%
Percentage of number sentenced to total Prison population=
𝑁𝑢𝑚𝑏𝑒𝑟 𝑠𝑒𝑛𝑡𝑒𝑛𝑐𝑒𝑑𝑑
𝑃𝑟𝑖𝑠𝑜𝑛 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑛
72798
100 = 81943 = 88.8%
Percentage of number of non-criminal prisoners to total Prison
𝑁𝑜𝑛−𝑐𝑟𝑖𝑚𝑖𝑛𝑎𝑙𝑠
767
population=𝑝𝑟𝑖𝑠𝑜𝑛 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 × 100 = 81943 × 100 = 1.0%
= 1%.
×
Bibliography
Croft, A. and Davison, R., (2016) Foundation Maths. 7th Edition. Harlow: Pearson. Available
at: https://bibliu.com/app/?query=foundation%20maths#/view/books/9781292289731/pdf2htmle
x/index.html#page_vii
Nash, T., Jones, K., Urtis, T. and Jelen, B. (2012) Don’t Fear the Spreadsheet. Uniontown, OH:
Holy Macro! Books. Available
at: https://bibliu.com/app/?query=spreadhseet%20don%27t%20fear#/view/books/978161547326
7/epub/OEBPS/DFSSePub-7.html#page_9
Neill, H. and Johnson, T. (2018) Mathematics: A Complete Introduction. London: John Murray
Press. Available at:
https://bibliu.com/app/#/view/books/9781473678361/epub/OPS/contents.html#page_3