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Unit 7: Numeracy skills

Approximating and Estimating

Example 2

The following table shows the number of items sold in one year by the Beans Co. in each of its operating districts. Column Y shows the number of salespeople employed in each
district.

Column X
Column Y
Column Z
District
Number of salespeople
Number of 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

  • Mid and SE have similar numbers of salespeople, but Mid sold far fewer items. Hence Mid can be eliminated.
  • SW sold fewer items than NW, but had far more salespeople. Hence SW can be eliminated.
  • The districts ‘ left in ‘ for consideration are SE, NW, NE
  • 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

Creative Commons License
SMILE - Numeracy skills by Tom Frank, Eric Williams and Clare Wright, University of Birmingham Careers Centre adapted by Marion Kelt Glasgow Caledonian University is licensed under a Creative Commons Attribution 3.0 Unported License.