Numeracy and Data Analysis: Solved Questions and Answers

This document contains solved questions and answers on Numeracy and Data Analysis. It includes step-by-step calculations for index numbers, mean, mode, median, range, and standard deviation. The content covers various topics such as individual income, consumer price index, and daily sales of a soft drink over a period of 10 days.

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