The Advanced Numeracy Test Workbook - Mike Bryon [4]
Powers A square number is a whole number raised to the power of 2. A cubed number is a whole number raised to the power of 3.
Numbers can be raised to any power. The values get big very quickly. Use the xy or yx functions on a calculator to calculate powers. Be able to recognize the sequence of low value powers:
22 – 27
4, 8, 16, 32, 64, 128
32 – 36
9, 27, 81, 243, 729
42 – 45
16, 64, 256, 1,024
52 – 55
25, 125, 625, 3,125
To multiply powers with common base numbers simply add the powers:
62 × 65 = 67
To divide powers with common base numbers subtract the powers.
Reciprocals If a number is divided into 1 you identify its reciprocal value. Some reciprocal values are better expressed as fractions because as decimals they are re-occurring. Be familiar with the convenient reciprocal values in the range 1–32:
2 = 0.5
4 = 0.25
5 = 0.2
8 = 0.125
10 = 0.1
16 = 0.0625
20 = 0.05
25 = 0.04
32 = 0.03125
The key terms in data interpretation
Mode is the value that occurs most frequently. The mode of the following data is 2 because it occurs five times:
2, 2, 2, 3, 3, 1, 2, 3, 1, 2, 3
The mode value of the following grouped data is the group 11–20:
Data group
Frequency
1–10 3
11–20 4
21–30 3
The median is the middle value when all the responses are arranged numerically. The median of the following values is 4:
10, 2, 8, 6, 4, 3, 1
The median divides the data into 2.
Learn the formula:
Median = ½ (n + 1)th value
The mean is the numerical average and is found by adding up all the values and dividing the sum by the number of values.
The mean of the following wages is
Wages
12,000
10,000
23,000
15,000
This example illustrates how an exceptionally high (or low) value (here 23,000) can distort the mean.
To approximate the mean of grouped data the mid-point (mid-interval value) of each group can be used.
Range is the distribution between the lowest and highest value. Range is also distorted by exceptional values.
Quartiles divide the distribution into four equal parts.
To identify the lower quartile use the formula:
¼ (n + 1)th value
To identify the upper quartile use:
¾ (n + 1)th value
The interquartile range examines only the middle two quartiles so avoids the distortions of exceptional values (these would lie in the upper or lower quartiles).
Minus the lower quartile value from the upper quartile value to obtain the value of the interquartile range.
A percentile divides the distribution into 100 equal parts.
If a relationship exists between two items a correlation is said to exist. When plotted, a curve or straight line will emerge and is taken as evidence of a correlation.
Distribution of data is often shown as a standard deviation. It takes account of all the values and provides an interpretation of the extent to which the data deviates from the mean.
In the workplace, specialist statistical software is likely to be used to calculate the standard deviation. But go to a psychometric test able to recognize the formula used:
Percentages To change a decimal into a percentage multiply it by 100. To express a fraction as a percentage again multiply it by 100. To convert a percentage into a decimal divide by 100.
To work out a percentage of something without a calculator try finding 1 per cent of the item and then multiply to get the answer. Alternatively convert it into a decimal or fraction and again multiply it.
Ratios are used to compare quantities. They are expressed in their lowest whole numbers. For example:
If there are 14 beads on a necklace, 6 of which are blue and 8 of which are red, then the ratio between blue and red beads is 6:8, which simplifies to 3:4.
Simple interest is the amount earned or paid on a sum invested (the principal amount). To calculate it you need to know the principal amount, the annual rate of interest and the length of time the interest is earned.
Principal +
(principal × rate × period)
100
Compound interest involves the reinvestment of the earned interest, which in future years also earns interest.
If the amount is only for a