Grouped Data

# Grouped Data

GCSE(F),

Data can be grouped into class intervals. A survey of companies found the number of employees for each company was:

EmployeesNumber of Companies
1 - 51
6 - 103
11 - 1516
16 - 204
21 - 251

The Modal Class is the class with the highest frequency: in this case, the modal class is 11 - 15.

The median is the class that contains the middle member. There are 25 companies; the middle company will be the 13th:

EmployeesNumber of CompaniesRunning count of companies
1 - 511
6 - 1034
11 - 151620
16 - 204
21 - 251

The 13th company is found in the class 11 - 15; this is the class interval of the median.

The Estimated Mean can be found by multiplying the Midpoint of the class interval by the frequency. The mean is estimated because any actual values are replaced by the midpoint value:

EmployeesFrequency fmidpoint mf x m
1 - 5133
6 - 103824
11 - 151613208
16 - 2041872
21 - 2512323
TOTALS25330

The estimated mean is 330 ÷ 25 = 13.2 employees.

The Range is the difference between the lowest possible value and the highest possible values: 25 - 1 = 24

A table may show class intervals with a simple range (e.g. 1 - 6) when the data is discrete; or as an inequality (e.g. 1 < x ≤ 6) when the data is continuous.

## Examples

1. The information, below, shows how long employees took to travel to work. Give an estimated mean of the travel time to work.

Travel Time (mins)Employees
0 < m ≤ 2022
20 < m ≤ 4015
40 < m ≤ 608
60 < m ≤ 802

From the table below, estimated total number of minutes for all employees = 1210. Number of employees = 27.

Estimated mean = 1210 ÷ 27 = 44.81 minutes

Travel Time (mins)Employees (e)Midpoint (m)e x m
0 < m ≤ 202210220
20 < m ≤ 401530450
40 < m ≤ 60850400
60 < m ≤ 80270140
TOTALS271210

2. The table below shows the journey time for employees arriving at work for a company. What is the modal class?

Travel Time (mins)Employees
0 < m ≤ 2022
20 < m ≤ 4015
40 < m ≤ 608
60 < m ≤ 802

Answer: 0 < m < 20

The modal class is the class interval with the highest frequency (22).