CIMA - C3 Fundamentals Of Business Mathematics
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390 Answer bank
B = 220 + 124 + 340 + 278 = 962
C = 944 ÷ 4 = 236.0
D = 962 ÷ 4 = 240.5
E = (236.0 + 240.5) ÷ 2 = 476.5 ÷ 2 = 238.25
F = 124 – 238 = –114
(b) G =
–2
H =
+0.5
I =
–12.5
J =
–112.0
K =
+102.0
L =
+22.5
Workings
Quarter
Year
1
2
3
4
Total
20X2
+101
+18
20X3
–11
–111
+102
+26
20X4
–15
–114
Average seasonal variation
–13.0
–112.5
+101.5
+22.0
–2
Adjustment
+0.5
+0.5
+0.5
+0.5
+2
Adjusted seasonal variation
–12.5
–112.0
+102.0
+22.5
0
The seasonal variations from the table in (a) are the initial entries in the table shown above. The
seasonal variations are averaged by adding them together and dividing by two. The total of the
averages gives the value of G, which should ideally be zero. (In this case it is –2.) We adjust the
average seasonal variations by subtracting G/4 (–2/4 = –0.5) from each average which in this case
means adding H = 0.5 in order to obtain the adjusted seasonal variations I to L.
(c)
255.5
Workings
The additive model is A = T + S and we seasonally adjust the data in order to estimate the trend, T.
T = A – S
= 278 – 22.5
= 255.5
Answer bank 391
(d)
232.5
Workings
The additive model is A = T + S. Forecast sales are calculated by adding the adjusted seasonal
variation (S) to the predicted trend (T).
Forecast sales = 245 – 12.5
= 232.5
97
172
Working
In Q3 of 2010, t = 19
T = 52 + (6.3 × 19) = 171.7
= 172 to three significant figures
98 A For week 9, the trend value is 84 + (0.7 × 9) = 90.3
The seasonal variation is actual – trend = 88.7 – 90.3
= – 1.6
99 D The residual is the difference between the actual data and the figure predicted by the time series
analysis. It is the unexplained element in the actual figure.
Actual
4,000
Trend (3,150 + 72 × 12)
4,014
Seasonal variation
(47
)
(3,967
)
33
100 D No computer system knows exactly what you intended so can not make 100% accurate connections.
101 B Microsoft Access is a database application.
102 B The current time and date will be displayed in the cell.
392 Answer bank
393
Index
394
395
Additive model, 284, 292
AND law, 172
Annual percentage rate (APR) of interest, 217
Annuity, 244, 247
factors, 247
formula, 245
tables, 247
Arithmetic mean, 118
of combined data, 120
of grouped data, 119
of ungrouped data, 118
Array, 124
AVERAGE function, 254
Average relatives indices, 157
Bar chart, 87
Base period, 150
Base year, 150
Brackets, 10
Chain base method, 152
Chart Wizard, 61
Charts, 87
Cluster sampling, 79
Coefficient
of determination, r
2
, 266, 267
of variation, 140
Complementary outcomes, 170
Component bar chart, 88
Composite index numbers, 156
Compound bar chart, 90
Compound interest, 212, 213
when there are changes in the rate of interest, 216
Conditional events, 175
Conditional probability, 175
Contingency tables, 176
Continuous data, 75
Correlation, 262
and causation, 267
coefficient, 264
Cost of capital, 235, 237
Cube root, 19
Cumulative frequency
curve, 105
diagram, 105
distribution, 100
polygon, 105
Cumulative present value factors, 247
Curve fitting, 108
Cyclical variations, 284
Data, 72
Data input forms, 309
Data types, 74
Deciles, 134
Decimal places, 6
Decimals, 4, 40
Deflation, 155
Degrees of correlation, 262
Dependent events, 175
Dependent variable, 51
Depreciation, 215
Deseasonalisation, 295
Discounted cash flow (DCF), 237
Discounting, 234
formula, 235
Discounts, 14
Discrete data, 75
Dispersion, 135
Downward-sloping ogives, 106
Equations, 45
Errors, 23
Excel functions, 307
Expected net present value, 239
Expected value, 178
Final value, 219
Fixed base method, 152
FORECAST function, 274
Forecasting, 296
Formulae, 44
in Excel, 25
Fractions, 4, 40
Frequency distributions, 97
FREQUENCY function, 111
Function key F4, 32
General rule
of addition, 173
of multiplication, 175
Geometric progression, 220, 221, 227
Gradient, 53
Graphs, 52
Grouped data, 138
Grouped frequency distributions, 97
396 Index
Histogram, 101, 111
IF statements, 38
Independent events, 172
Independent variable, 51
Index, 150
numbers, 150
points, 150
relative, 150
Inequalities, 49
Inflation, 215
Information, 72
INSERT COMMENT, 308
Integer, 4, 40
Intercept, 53
Internal rate of return (IRR) method, 241
Interpolation, 241, 242
Inter-quartile range, 133
Investment appraisal, 237, 253
IRR, 241, 243
function, 254
Laws of probability, 169
Learning curve formula, 45
Least squares method of linear regression analysis,
271
Limitations
of expected values, 184
of forecasting models, 299
Linear equation, 51
Linear regression analysis, 271
Lines of best fit, 269
Loans, 225
Lower quartile, 132
Macros, 309
Mean, 118
deviation, 135
Measures of central tendency, 145
Measures of dispersion, 145
Median from an ogive, 126
Median, 124, 132
of a grouped frequency distribution, 126
of an ungrouped frequency distribution, 126
Modal value, 122
Mode, 122
from a histogram, 123
of a grouped frequency distribution, 122
Mortgage, 227, 252
repayments, 227
Moving average, 285
Moving average
method, 285
of an even number of results, 287
of an odd number of results, 285
Multiple bar chart, 90
Multiplicative model, 284, 292
Multistage sampling, 78
Mutually exclusive outcomes, 171
Naming a range of data, 144
Negative correlation, 263
Negative numbers, 4
Negatively skewed distribution, 143
Net Present Value (NPV) method, 237
Nominal rates of interest, 217
Non-linear equations, 57
Normal distribution, 190, 191
tables, 192
NOW, 307
NPV function, 254
n
th
root, 19
Ogive, 104, 112
OR law, 170
Order of operations, 10
Parabolas, 59
Pareto analysis 80/20 rule, 201
Partial correlation, 263
Payoff tables, 182
Percentage changes, 14
Percentage component bar chart, 89
Percentages, 11
Perfect correlation, 262
Perpetuity, 247
Pie chart, 93
Positive correlation, 263
Positively skewed distribution, 142
Power (^), 19, 26
Present value, 234
of a perpetuity, 247
of an annuity, 244
tables, 236
Price index, 150
Price relative, 151, 157
Primary data, 75
Index 397
Probability, 168
distribution, 190
Probability of achieving the desired result, 169
Product moment correlation coefficient, 264
Profits, 15
Project comparison, 239
Proportion, 17
Proportional model, 292
Quadratic equations, 58
Qualitative data, 72
Qualitative information, 73
Quantitative data, 72
Quantitative information, 73
Quantity index, 150
Quantity relative, 151
Quartile, 132
deviation, 133
Quota sampling, 79
Random sampling, 77
Range, 132, 145
Rank correlation coefficient, 267
Ratios, 18
Reciprocals, 5
Reducing balance depreciation, 215
Regression, 269
Regular savings, 219
Repayment mortgage, 227
Residual, 299
Retail prices index (RPI), 160
Return on investment, 254
Reverse compounding, 215
Risk and uncertainty, 184
Roots, 19
Round, 29
RPI, 160
Sampling, 76
Savings funds, 219
Scatter diagrams, 107, 262
Scattergraph, 273
method, 269
Scientific calculator, 7
Seasonal variations, 283
Seasonally-adjusted data, 295
Secondary data, 75
Semi inter-quartile range, 133
Sigma Σ, 119
Significant figures, 5, 6
Simple addition law, 170
Simple bar chart, 87
Simple interest, 212
Simple linear regression, 269
Simple multiplication law, 172
Simple probability, 169
Simultaneous equations, 56
Sinking fund, 219, 223, 250
Skewed distributions, 142
Skewness, 142
Spearman's rank correlation coefficient, 267
Splicing, 153
Spreadsheet, 24, 306
design, 308
Square root, 19
Standard deviation, 138, 145, 191
for grouped data, 138
for ungrouped data, 138
Stratified random sampling, 77
SUM, 27
Symmetrical frequency distribution, 142
Systematic sampling, 78
Tables, 86
Tabulation, 86
Templates, 309
Terminal value, 219
Tied ranks, 268
Time series, 282
analysis, 285
deflation, 155
of index relatives, 152
Trend, 282
line, 108
Unequal class intervals, 101
Ungrouped data, 138
Upper quartile, 132
Variance, 137, 138, 145
for grouped data, 138
for ungrouped data, 138
Venn diagrams, 169
Weighted average of price relative index, 158
Weighted average of quantity relative index, 158
Weighted average of relatives indices, 158
Weighted index numbers, 158
398 Index
Z score, 195
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