Frequency Tables

 

These are a useful way of collating raw data,

to quickly see the mode, find the median

 and calculate the mean.

 

Example

 

A manufacturer claims that each packet of shazbo

contains 20 sweets on average.

 

When 30 packets of Shazbo are examined,

the results are as follows :-

 

No. of sweets per packet

 

18  17  22  19   20   20   21  19  18   20

21  19  21  19   20   20   20  17  19   21

22  18  17  16   20   20   20  21  21  20

 

Is the manufacturer correct ?

 

 

 

Construct a frequency table of the data.

 

 

No.ofSweets	Tally	Frequency
16	ι	1
17	ιιι	3
18	ιιι	3
19	ιιιι	5
20	ιιιι  ιιιι	10
21	ιιιι  ι	6
22	ιι	2
	Total	30

 

 

The table shows that the mode of the sample is

20 sweets, which has a frequency of 10.

 

 

The median value lies half way between the

15^th and 16^th values.

No.ofSweets	Tally	Frequency
16	ι	1
17	ιιι	3
18	ιιι	3
19	ιιιι	5
20	ιιιι  ιιιι	10
21	ιιιι  ι	6
22	ιι	2
	Total	30

 

Adding the frequency column shows

that the first 12 values have between 16

and 19 sweets.

 

The 15^th and 16^th values have 20 sweets.

The median is therefore 20 sweets.

 

 

 

To calculate the mean , we need to add another column

 and multiply the frequency by the number of sweets.

 

Data No.ofSweets	Tally	Frequency	Frequency x data
16	ι	1	16
17	ιιι	3	51
18	ιιι	3	54
19	ιιιι	5	95
20	ιιιι  ιιιι	10	200
21	ιιιι  ι	6	126
22	ιι	2	44
	Total	30	586

 

 

The mean is 19½ sweets,

 which could be rounded to 20 sweets.

 

 

 

The manufacturer is correct !!