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district. Column X Column Y Column Z District Number of Number of salespeople items sold SW 57 53,971 NW 38 64,562 Mid 31 21,123 SE 27 47,051 NE 23 42,510 Task 1. In which district was the highest number of items sold per salesperson? Task 2. In which district was the lowest number of items sold per salesperson? Steps: i. To make handling of figures more manageable, make approximations of the items sold figures. Approximation table District Salespersons Items sold (in thousands) SW 57 54 NW 38 64.5 Mid 31 21 SE 27 47 NE 23 42.5 Approximation and comparison can eliminate certain districts from the need to calculate accurately. Task 1. The highest average sales i. Mid and SE have similar numbers of salespeople, but Mid sold far fewer items. Hence Mid can be eliminated. ii. SW sold fewer items than NW, but had far more salespeople. Hence SW can be eliminated. iii. The districts ‘ left in ‘ for consideration are SE, NW, NE iv. Use a calculator to do the division, USING THE ACCURATE FIGURES, to find the averages of the 3 districts. SE 47,051/27 = 1742.6 NW 64,562/38 = 1699 NE 42,510/23 = 1848 Hence the highest average sales figures per salesperson was in the NE district. Task 2. The lowest average sales per person per district From your approximation table it is evident that Mid sold far fewer items than each of NW,SE,NE, despite having similar numbers of salespeople. It is not so clear as to how Mid compares with SW, so two calculations are desirable. SW 53,971/57 = 946.86 Mid 21,123/31 = 681 Hence Mid district had the lowest average number of items sold per salesperson SECTION 4 – AVERAGES There are several ways of expressing an average. The most common way is called a mean . This is one value which is representative of all the numbers in a group. The mean is calculated by adding up all the numbers in a group, then dividing by how many numbers there are. Example 1 Find the average, or mean, of the following numbers: Mean = 2+6+4+8+5+5 = 30 = 5 6 6 Check your answer – is an answer of 5 representative of the numbers? Example 2 Find the average, or mean, of the following numbers: 1 3 4 2 1 20 Mean = 1+3+4+2+1+20 = 31 = 5.17 6 6 Check your answer – in this case, most of the numbers are less than 5 but the very high value of 20 pulls the mean upwards, so the answer is sensible. Example 3 In a test of numerical ability, students are tested in two groups. Which group has the higher average score? Group A Group B 3 7 15 6 8 10 9 11 12 19 13 20 3+15+8+9+12+13 7+6+10+11+19+20 6 6 = 60 = 73 6 6 = 10 = 12.17 Group B has the higher average score TRY THESE QUESTIONS: Find the mean of each of these sets of data: 1. 2 4 6 7 4 3 5 2. 49 50 63 61 67 59 73 68 42 3. 6 7 8 7 8 6 4. 15 16 12 19 14 20 18 17 18 16 5. 107 109 117 119 112 6. Which group of students scored best in this numerical reasoning test? Group A: 11 12 13 6 18 17 4 12 10 15 Group B: 10 11 9 12 14 13 12 10 11 14 7. A lecturer decided to find out how punctual students really are. He recorded how late his seminar group arrived on three occasions. The table shows how many minutes late each of the ten students were on these days. What was the overall average lateness? Which day was worst? On which day were most students more than 5 minutes late? Day 1 Day 2 Day 3 2 5 4 0 10 1 4 8 3 15 6 0 10 0 0 4 0 5 5 10 4 0 9 1 0 0 0 1 0 15 Answers on page 20 SECTION 5 - PERCENTAGES Percentage is one of three ways of expressing a value e.g. 17% has the same value as 17/100 or 0.17 It is recommended that, before using the calculator, you first understand, through mental calculation, the principles of layout of expressions and the functions of addition, subtraction, multiplication and division in fractions and decimals. Percentage and decimal - the relationship Examine the ‘meaning’ of the figure 425. 631. The position of each digit gives it its value. Regard each digit as being a member of a column （责任编辑：职场达人） |
