IBBusiness ManagementSLRevision Notes6. The Business Management Toolkit6.1 The Business Management Toolkit6.1.7 Descriptive Statistics

Descriptive Statistics (SL IB Business Management)

Revision Note

Lisa Eades

Mean, Median & Mode

  • Simple statistical analysis may include calculating the average of a given set of numerical data, using one of three methods
    • The mean is commonly considered the true average - where all the numbers in a data set are added and then divided by the number of numbers
    • The median is the middle value in the list of numbers
    • The mode is the value that occurs most often in a set of data

Worked example

RapidKleen kept a record of mobile vehicle valets carried out each day during a busy holiday period.

Find the mean, median, mode, and range of mobile valets during the period using the following data.


Day


1
2
3
4
5
6
7
8
9

No. of valets sold
13
18
13
14
13
16
14
21
13


[6 marks]

Step 1: To calculate the mean, first add together each of the values

13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13 = 135

Step 2: Divide the total by the number of values

135 ÷ 9 = 15

[2 marks]

  • Note that the mean in this case isn't a value from the original data set
  • This is a common result - you should not assume that your mean will be one of your original numbers and you should not be surprised when it isn't

Step 3: To calculate the median first rewrite the data set in numerical order

13, 13, 13, 13, 14, 14, 16, 18, 21

Step 4: Identify the middle number

  • There are nine numbers in the list, so the middle one will be the (9 + 1) ÷ 2 = 10 ÷ 2 = 5th number:

13, 13, 13, 13, 14, 14, 16, 18, 21

So the median is 14

[2 marks]

  • Note: The formula for the place to find the median is "([the number of data points] + 1) ÷ 2", but you don't have to use this formula
    • You can just count in from both ends of the list until you meet in the middle if you prefer, especially if the data set is small

Step 5: To calculate the mode rewrite the data set in numerical order

13, 13, 13, 13, 14, 14, 16, 18, 21

Step 6: Identify the number that occurs most often in the list

13 occurs four times

14 occurs twice

16 appears once

18 appears once

21 appears once

As it appears most frequently the mode number of valets sold is 13

[2 marks]

Standard Deviation

  • The standard deviation is a measure of the spread of numbers within a set of data
  • It is a particularly useful tool for planning when managers have wide ranges of data and need to organise resources effectively

Worked example

FreshBite is a pre-packaged sandwich manufacturer which produces a range of products that are sold in cafés and refreshment stands in tourist attractions such as theme parks.

Freshbite's sales are highly variable - the business regularly suffers from high levels of wastage as a result of having large quantities of unsold stock. On several occasions it has also been unable to fulfill orders from customers as it has not produced enough units.

The business has recently employed a new operations manager who has suggested that calculating the standard deviation of sales would aid planning. He has requested the last month's sales data to allow him to calculate this.


Product
Last month's sales ($)
A 110,000
B 27,000
C 12,000
D 54,000
E 7,000

Calculate the standard deviation of last months' sales for Freshbite. 

[4 marks]

Step 1: Calculate the mean

110,000 + 27,000 + 12,000 + 54,000 + 6,000 = 210,000

210,000 ÷ 5 = 42,000

[1 mark]

Step 2: For each product, subtract the mean and square the result


Product
Last month's sales ($000s)


Minus mean =


Squared = 
(000's)
A 110 68 4,624
B 27 -15 225
C 12 -30 900
D 54 12 144
E 7 -35 1,225

[1 mark]

Step 3: Add up the squared differences and express in an expanded form

4,624 + 225 + 900 + 144 + 1,225 = 7,118

= 7,118,000

[1 mark]

Step 4: Find the square root to identify the standard deviation 

square root of 7 comma 118 comma 000 space end root space equals space $ 2667.96

[1 mark]


Note - in this instance, a significant standard deviation from the mean informs Freshbite's managers that they need to carefully plan for significant variations in sales. This may include detailed market research as well as capital investment to reduce wastage (for example, further freezers).

Quartiles

Quartiles

  • Quartiles are the values that divide a list of numbers into quarters
  • Analysis of data using quartiles allows a business to see the distribution and spread of data 
    • The first quartile is the lower 25% of a list of numbers
    • The second quartile is the lower 50% of a list of numbers
    • The third quartile is the lower 75% of a list of numbers
    • The top quartile is the highest 25% of a list of numbers
    • The interquartile range excludes outlying data in the top and bottom quartiles and examines the middle spread of data

The Application of Quartile Ranges to a set of data

First Quartile  
Second Quartile  
Third Quartile  
  Top Quartile
  Interquartile Range  
3 3.5 4.5 5 6 6.5 7.5 8

Worked example

BestGrip is shoe manufacturing business that employs a team of sales managers who receive performance-related monthly bonuses on top of their monthly salaries.

Bonuses are awarded to those sales managers who achieve sales in the top quartile.

Sales data for the month of May are shown in the table below.


Salesperson
Volume of Sales
A 24,300
B 25,350
C 26,650
D 22,100
E 26,200
F 27,800
G 22,950
H 28,450
I 23,750
J 29,200
K 27,350
L 27,900

Identify the sales managers to be awarded a bonus in May.

[4 marks]

Step 1: Put the list of data into order, from smallest to largest

Salesperson Volume of Sales
D 22,100
G 22,950
I 23,750
A 24,300
B 25,350
E 26,200
C 26,650
K 27,350
F 27,800
L 27,900
H 28,450
J 29,200

[2 marks]

Step 2: Divide the list into four equal parts:

Salesperson Volume of Sales  
D 22,100
Quartile 1
G 22,950
I 23,750
A 24,300
Quartile 2
B 25,350
E 26,200
C 26,650
Quartile 3
K 27,350
F 27,800
L 27,900
Quartile 4
H 28,450
J 29,200

[1 mark]

Step 3: Identify the data within the top quartile

  • In this case, sales managers L, H and J will receive a performance-related bonus in May

[1 mark]

Graphs & Charts

  • Analysis of data contained in graphs and charts and the communication of complex data in these forms are important business skills
  • Data may be presented in a range of forms

1. Bar charts

  • Bar charts show data that are independent of each other such as sales per store

screen-shot-2023-07-03-at-10-58-42-am

An example of a bar chart showing sales revenue of a selection of home video entertainment formats in the USA in 2017

(Source: British Council)


2. Pie charts 

  • Pie charts show how a whole is divided into different elements such as total sales divided amongst different product types
  •  screen-shot-2023-07-03-at-11-35-11-am
  • An example of a pie chart showing Apple's quarterly revenue by category in April 2021
  • (Source: Six Colours)
      

3. Infographics 

  • Infographics are easy to understand visual representations of data

screen-shot-2023-07-03-at-11-55-50-am

An example of an infographic used by Mars to communicate key business statistics

(Source: Mars)

Worked example

Maggri Spice Ltd manufactures a range of hot curry pastes that are sold online and in specialist stores.

In 2022 total sales were $180,000, with sales for individual products shown in the pie chart below.

Sales share of Maggri's different products

Calculate the value of sales of Blue Heat curry paste in 2022.

[2 marks]

Step 1: Identify the percentage of total sales attributed to Blue Heat

In this case 23.9% of total sales can be attributed to Blue Heat

Step 2: Convert the percentage to a decimal

23.9% = 0.239

[1 mark]

Step 3 - Multiply total sales by the decimal

$180,000 x 0.239 = $43,020

Blue Heat curry paste achieved sales of $43,020 in 2022

[1 mark]

Exam Tip

You can make use of descriptive statistical techniques throughout both exam papers.

They are particularly useful when making comparisons or supporting chains of analysis to lead to a judgement. You do not have to wait to be told to use them in your work - become accustomed to applying them to data in your work as you move through the course.

Interpreting data using these tools is a higher level approach to application and demonstrates that you are making optimum use of data presented in case study materials - this really does impress the examiner!

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    Lisa Eades

    Author: Lisa Eades

    Lisa has taught A Level, GCSE, BTEC and IBDP Business for over 20 years and is a senior Examiner for Edexcel. Lisa has been a successful Head of Department in Kent and has offered private Business tuition to students across the UK. Lisa loves to create imaginative and accessible resources which engage learners and build their passion for the subject.