Grouped Data3012

Now read this:

  • When we have a wide range of data, it is convenient to organise the data into classes. These show a range of data. It is less accurate to use classes, because the exact value of the data is lost. However, it can save a lot of work. Making a tally can help reduce mistakes.
  • When data is in classes it is easy to see the modal class. This is the class with the highest frequency. Also, the class which contains the median is called the median class.

Read carefully though this example.

Make sure that you understand.

A factory has a census of its workers. There are 50 workers in total. The following list shows their ages:

34, 28, 22, 36, 27, 18, 52, 39, 42, 29, 35, 31, 27, 22, 37, 34, 19, 20, 57, 49, 50, 37, 46, 25, 17, 37, 42, 53, 41, 51, 35, 24, 33, 41, 53, 60, 18, 44, 38, 41, 48, 27, 39, 19, 30, 61, 54, 48, 26, 18.

(a)Make a table grouping the data into classes from 10 to 19,

20 to 29, 30 to 39, 40 to 49 etc. Find the modal and median classes.

(b)Make a table grouping the data into classes from 15 to 19,

20 to 24, 25 to 29, 30 to 34, 35 to 39 etc. Find the modal and median classes.

Solution

(a) / Age / Tally / Number of workers
10-19 / //// / / 6
20-29 / //// //// / / 11
/ 30-39 / //// //// //// / 14
40-49 / //// //// / 10
50-59 / //// // / 7
60-69 / // / 2

The modal class is 30-39 years old.

There are 50 workers. So the median will be the 25th and 26th workers. Count up from the tally chart. The 25th and 26th workers are both in the 30-39 class.

So, the median class is also 30-39 years old.

(b) / Age / Tally / Number of workers
15-19 / //// / / 6
20-24 / //// / 4
25-29 / //// // / 7
30-34 / //// / 5
35-39 / //// //// / 9
/ 40-44 / //// / / 6
45-49 / //// / 4
50-54 / //// / / 6
55-59 / / / 1
60-64 / // / 2

The modal class is now 35-39 years old.

The 24th and 25th workers are both in the 35-39 class.

So, the median class is also 35-39.

Now answer these questions.

2.The data shows the marks given to a class of mathematics students in a test.

34, 12, 45, 23, 12, 18, 26, 41, 48, 23, 47, 11, 7, 15, 31, 28, 6, 43, 27, 38, 32, 21, 29, 45, 15, 9, 20, 37, 43, 27, 30, 17, 14, 26, 34, 24, 18, 16, 35, 32, 27, 14, 30, 22, 31, 40, 17, 24, 37, 13

Copy the tally chart below.

Complete the tally. Cross off each number in the list as you use it.

Mark / 1-10 / 11-20 / 21-30 / 31-40 / 41-50
Tally
Total

Check that the totals add up to 50 students.

Write down the modal class.

3.The data shows the ages of 20 workers in an office.

23, 35, 21, 20, 28, 32, 19, 39, 20, 18,

37, 29, 19, 25, 34, 26, 24, 31, 22, 30.

(a)Make a tally chart with classes for 16-20, 21-25, 26-30, 31-35 and 36-40.

(b)Check that the total adds up to 20.

(c)Write the data in order and find the median.

(d)Which class is it in ? (This is the median class).

(e)Write down the modal class.

4.A scientist measures the weights of 20 tomatoes (in grammes) in an experiment. These are the results:

121, 187, 143, 219, 191, 146, 203, 142, 172, 234, 163, 194, 241, 150, 125, 219, 162, 210, 120, 236.

(a)Make a table for this data using classes from 120-149, 150-179, 180-209, 210-229 and 230-259.

(b)Find the modal class.

(c)Find the median class.

8.A machine measures the length of a part in a tractor engine. The measurements (in millimetres) are to the nearest 01 mm.

111, 113, 107, 112, 116, 109, 106, 113, 112, 105,

104, 112, 111, 116, 106, 113, 109, 112, 110, 114.

(a)Make a table for classes 101-105, 106-110 etc.

(b)What is the modal class ?

(c)What is the median class ?