given below is a cumulative frequency distribution of less than type. change the given data into a continuous grouped frequency distribution.
Answers
Cumulative Frequency Distribution of Discrete Variable
Let us refer to the following frequency distribution:
Number of car accidents Frequency
3 5
4 9
5 11
6 4
7 1
Total 30
The cumulative frequency distribution will be:
Number of car accidents Frequency Cumulative Frequency Relative Frequency Cumulative Relative Frequency
(< type) (> type) (< type) (> type)
3 5 5 30 0.17 0.17 1.00
4 9 14 25 0.30 0.47 0.83
5 11 25 16 0.37 0.84 0.53
6 4 29 5 0.13 0.97 0.16
7 1 30 1 0.03 1.00 0.03
Total 30 – – 1.00 – –
The Cumulative Frequency (< type) corresponding to the value 3 is 5 which means that the number of values less than or equal to 3 is 5. Similarly the Cumulative Frequency (< type) corresponding to the value 6 is 29 which means the number of values
\leq 6 is 5+9+11+4=29, i.e., there are 29 values less than or equal to 6. Similarly, the Cumulative Frequency (> type) corresponding to the value 6 is 5 which means the number of values
\geq 6 is 4+1=5, i.e., there are 5 values greater than or equal to 6.
If we want to find out the proportion of values less or greater than a particular value we refer to the Cumulative Relative Frequency columns. The Cumulative Relative Frequency (< type) corresponding to 4 is 0.47 which means that the number of values less than or equal to 4 is 0.47 part of the total number of values. Again, Cumulative Relative Frequency (> type) corresponding to 4 is 0.83 which means that the number of values greater than or equal to 4 is 0.83 part of the total number of values.
If the distribution of the discrete variable be a grouped frequency distribution the cumulative frequencies, instead of corresponding to individual values will correspond to the class boundaries. The Cumulative Frequency (< type) corresponds to the upper class boundaries of each class and the Cumulative Frequency (> type) corresponds to the lower class boundaries of each class.
It should be noted that the Cumulative Frequency (< type) corresponding to the highest value and the Cumulative Frequency (> type) corresponding to the lowest value are both equal to the total frequency which is 30.
Cumulative Frequency Distribution of Continuous Variable
Let us refer to the following frequency distribution:
Class Intervals(Temperatures in
^{\circ}C ) Frequency
17-20 17
21-24 7
25-28 10
29-32 9
33-36 7
Total 50
The cumulative frequency distribution will be:
Class Intervals(Temperatures in
^{\circ}C ) Class Boundaries Frequency Cumulative Frequency Relative Frequency Cumulative Relative Frequency
(< type) (> type) (< type) (> type)
17-20 16.5-20.5 17 17 50 0.34 0.34 1.00
21-24 20.5-24.5 7 24 33 0.14 0.48 0.66
25-28 24.5-28.5 10 34 26 0.20 0.68 0.52
29-32 28.5-32.5 9 43 16 0.18 0.86 0.32
33-36 32.5-36.5 7 50 7 0.14 1.00 0.14
Total – 50 – – 1.00 – –
In case of a continuous variable, the distribution will always be grouped. Hence, for a continuous variable the cumulative frequencies, instead of corresponding to individual values correspond to class boundaries. The same rule is followed as in the case of grouped frequency distribution of a discrete variable. Cumulative Frequency(< type) corresponds to upper class boundaries and Cumulative Frequency(> type) corresponds to lower class boundaries.
Answer:
Marks obtained No.of students
10-20 8
20-30 5
30-40 6
40-50 5
Explanation :
10-20 : 8
20-30 : 13-8 = 5
30-40 : 19-13 = 6
40-50 : 24-19 = 5...