Comprehensive Numeracy and Data Analysis Assignment Solution

This document presents a comprehensive solution to a numeracy and data analysis assignment. The assignment covers a range of topics including percentage calculations, basic arithmetic operations, and the application of statistical concepts. Part A of the solution addresses questions involving percentage calculations, and various arithmetic problems. Part 2 delves into index numbers, calculating them with a base year, and exploring the significance of the consumer price index. The solution also includes calculations for mean, mode, median, range, and standard deviation using a provided dataset of daily sales figures. The calculations are presented step-by-step, ensuring clarity and ease of understanding. The assignment comprehensively covers the key concepts of data analysis and provides a detailed guide to solving related problems.

Numeracy and Data
Analysis

Contents
PART A......................................................................................................................................4
Question 1..................................................................................................................................4
Question 2..................................................................................................................................4
Question 3..................................................................................................................................5
Question 4..................................................................................................................................5
Question 5..................................................................................................................................5
PART 2.......................................................................................................................................6
QUESTION 2.............................................................................................................................6
a) Using 2015 as the base year (=100), find the index numbers for individual income over
the whole period. Show step by step calculations..................................................................6
QUESTION 5.............................................................................................................................7
The following table shows the daily sale of one the soft drink over 10 days’ period............7

PART A
Question 1
a) 1505 / (33 + 42) (2 * 5 - 8)
= 1505 / (9 + 16) (10 – 8)
= 1505 / (25) (2)
= 1505 / 50
= 30.1
b) (4374 / 272) (810 / 92)
= (4374 / 729) (810 / 81)
= (6) (10)
= 60
c) 400 / 5(5+3*2) – 420
= 400 / 5 (11) – 420
= 400 / 55 - 420
= 7.27 – 420
= -412.72
d) 3 * (602 / (3*22)) + (53 / 52)
= 3 * (3600 / (3*8)) + (125 / 25)
= 3 * (3600/25) + (5)
= 3 * (150) + 5
= 450 + 5
= 455
e) (729 / (15+12)) / 3 + 8 – 2 + ((42*3) / 2
= (729 / 27) / 3 + 8 – 2 + ((16 * 3) / 2)
= 27 / 3 + 8 – 2 + (48 / 2)
= 9 + 8 – 2 + (16)
= 17 – 2 + 16
= 31
Question 2
a) (-27) * (-5)
= 27 * 5
= 135
b) 32 – (-6)

= 32 + 6
= 38
c) (81) / 9 – (-6)
= -8 / 9 + 6
= - 9 + 6
= -3
Question 3
a) 3/5 + 3/8
= (24 + 15) / 40
= 39 / 40
= 0.975
b) 4/7 – 2/5
= (20 – 14) / 35
= 6 / 35
= 0.171
c) 22 / 5 + 25 / 8
= (176 + 125) / 40
= 301 / 40
= 7.525
Question 4
a) Black Pens = 100 – 46.7%
= 53.3%
Black pens = 42570 * (53.3/100)
= 22689.81 pens
b) Total Students = 28500
Student based in England = 28500 * (43.6 / 100)
= 12483 Sheets
Question 5
a) Total Investment = 165680
A = 165680 * (7/19) = 61040
B = 165680 * (3/19) = 26160
C = 165680 * (5/19) = 43600
D = 165680 * (4/19) = 34880

b) Y’s Investment = 21000
Total Investment = 21000 * (16/7) = 48000
X = 48000 * (4/16) = 12000
Z = 48000 * (5/16) = 15000
PART 2
QUESTION 2
Year Annual sales
(£000)
2014 6.8
2015 6.9
2016 7.2
2017 7.6
2018 7.1
a) Using 2015 as the base year (=100), find the index numbers for individual income over the
whole period. Show step by step calculations.
a) Index Number = (2017 sales / base year 2016) * 100
= (7.6 / 7.2) * 100 = 105.55
b) Index = 108.97
Sales of Base year = sales of 2015 / Index
= (6.9 / 108.97) * 100 = 6.33
c) Index = 82.63
Sales of Base year = sales of 2018 / Index
= (7.1 / 82.63) * 100 = 8.59
d) Significance of Consumer price index: CPI portrays what the progressions in cost
levels mean for heterogeneous clients. Likewise, it helps the public authority in
forming monetary approaches, cost arrangement, charge strategy, and so on.

Consequently, it helps the public authority in working out the dangers taken for
improvement without changing the cost for many everyday items.
QUESTION 5
The following table shows the daily sale of one the soft drink over 10 days’ period
Days Sales
in £
1 28
2 32
3 35
4 26
5 28
6 36
7 41
8 32
9 23
10 43
(i) Mean: It is the average of all the sales figure of 10 consecutive days.
Mean = sum of all observations / total no of observations
= 324/ 10 = 32.4
(ii) Mode = It is the highest number of times the sae value has occurred
Mode = 28
(iii) Median: It is the mid – value of data collected of the sales.
Median value = (N +1) / 2
(10 + 1) / 2 = 11 / 2 = 5.5
Median = (5th value + 6th value) / 2
= (32 + 32) / 2 = 64 / 2 = 32
(iv) Range = Maximum – Minimum
= 43 - 23 = 20
(v) Standard Deviation = √ (∑(𝑿−μ)2) / N
Standard deviation

Day Sales xi - μ (xi - μ)2
1 28 11.9 141.61
2 32 15.9 252.81
3 35 18.9 357.21
4 26 9.9 98.01
5 28 11.9 141.61
6 36 19.9 396.01
7 41 24.9 620.01
8 32 15.9 252.81
9 23 6.9 47.61
10 43 26.9 723.61
324 2.84 3031.3
Standard deviation = 6.118