# Mean Mode and Median Essay

935 Words Jan 17th, 2015 4 Pages
Mean, Mode and Median

Ungrouped and Grouped Data
Ungrouped Data refers to raw data that has been ‘processed’; so as to determine frequencies. The data, along with the frequencies, are presented individually.

Grouped Data refers to values that have been analysed and arranged into groups called ‘class’. The classes are based on intervals – the range of values – being used.
It is from these classes, are upper and lower class boundaries found.

Mean

Mean
The
 ‘Mean’ is the total of all the values in the set of data divided by the total number of values in a set of data.
The arithmetic mean (or simply "mean") of a sample is the sum the sampled values divided by the number of items in the sample.

 x is the value of a member of the set
Where: L is the lower class boundary, n is the total number of data, cfbis the cumulative frequency of the groups before, Fm is the interval frequency and W is the group width.

Let’s
 apply the formula:
 L=6.5
 n=52
 cfb = 14+9=23
 fm = 16
 W=3

Interval

Frequencies

1-3

14

4-6

9

7-9

16

10-12

13
52

= 21.5625

Understood?
Case Study:
A class of thirty students had a quiz. At the end of the class, the teacher posted the results. From the table on the right:
 Create a frequency table and

calculate the mean.

20

11

9

15

3

12

5

1

18

2

8

15

6

9

7

14

11

19

4

8

18

7

15

5

7

19

12

14

15

2

 Create a class frequency table and

provide the estimated mean – using a class width of 5.
 Determine the mode and median.
 Show the estimated median using

the grouped data (class frequency
table)

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