Question
Calculate the mode of the following frequency distribution:
|
Size of Items : |
|||||||||||
|
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
|
|
No. of Items : |
|||||||||||
|
2 |
3 |
6 |
12 |
20 |
24 |
25 |
7 |
5 |
3 |
1 |
|
Solution
On inspection we find that 12 is the mode but it does not appear to be correct since maximum items are not concentrated around. This value let us use the grouping method to determine mode.
Grouping Table
|
Size Item |
Col. 1 |
CoL 2 |
CoL 3 |
CoL 4 |
CoL 5 |
CoL 6 |
|
7 |
2 |
|||||
|
8 |
3 |
5 |
9 |
11 |
21 |
|
|
9 |
6 |
|||||
|
10 |
12 |
18 |
32 |
|||
|
11 |
20 |
56 |
38 |
|||
|
12 |
24 |
44 |
69 |
|||
|
13 |
25 |
49 |
56 |
|||
|
14 |
7 |
32 |
12 |
37 |
||
|
15 |
5 |
8 |
15 |
|||
|
16 |
3 |
4 |
||||
|
17 |
1 |
9 |
Analysis Table
|
Col. No. |
Size of Items |
||||||||||
|
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
|
|
1 |
1 |
||||||||||
|
2 |
1 |
1 |
1 |
||||||||
|
3 |
1 |
||||||||||
|
4 |
1 |
1 |
1 |
1 |
|||||||
|
5 |
1 |
1 |
|||||||||
|
6 |
1 |
1 |
1 |
||||||||
|
Total |
1 |
3 |
5 |
4 |
1 |
||||||
Since size 12 occur the maximum number of times i.e. 5 times the mode is 12.
