At the local movie theater entrance, group sizes were observed and recorded to better understand the social aspects of moviegoing. The findings are in the data below. Group Size, X 1 2 3 4 5 Frequency 2 47 2419 8 Relative Frequency 0.02 0.47 0.240.19 0.08 Which table correctly displays the cumulative relative frequencies of group size?
Group Size, X 1 2 3 4 5
Frequency 2 47 2419 8
Relative Frequency 0.02 0.47 0.24 0.19 0.08
To find the cumulative relative frequencies, we add up the relative frequencies of each group size and all smaller group sizes. The table that correctly displays the cumulative relative frequencies is:
Group Size, X 1 2 3 4 5
Cumulative Relative Frequency 0.02 0.49 0.73 0.92 1.00
The cumulative relative frequency of a group size is the proportion of all moviegoers that attended in a group of that size or smaller. For example, the cumulative relative frequency for group size 3 is 0.73, which means that 73% of moviegoers attended in a group of size 3 or smaller.
To find the cumulative relative frequencies, we need to add up the relative frequencies for each group size, starting from the smallest group size.
Using the given data, we can calculate the cumulative relative frequencies as follows:
Group Size: 1 -> Cumulative Relative Frequency: 0.02
Group Size: 2 -> Cumulative Relative Frequency: 0.02 + 0.47 = 0.49
Group Size: 3 -> Cumulative Relative Frequency: 0.49 + 0.24 = 0.73
Group Size: 4 -> Cumulative Relative Frequency: 0.73 + 0.19 = 0.92
Group Size: 5 -> Cumulative Relative Frequency: 0.92 + 0.08 = 1.00
Therefore, the correct table displaying the cumulative relative frequencies of group size would be:
Group Size | Cumulative Relative Frequency
1 | 0.02
2 | 0.49
3 | 0.73
4 | 0.92
5 | 1.00
To find the cumulative relative frequencies of the group size, you need to add up the relative frequencies for each group size starting from the smallest group size to the largest group size.
First, let's calculate the cumulative relative frequency for each group size:
Group Size | Relative Frequency | Cumulative Relative Frequency
-----------------------------------------------------
1 | 0.02 | 0.02
2 | 0.47 | 0.49 (0.02 + 0.47)
3 | 0.24 | 0.73 (0.49 + 0.24)
4 | 0.19 | 0.92 (0.73 + 0.19)
5 | 0.08 | 1.00 (0.92 + 0.08)
Therefore, the correct table that displays the cumulative relative frequencies of group size is as follows:
Group Size | Cumulative Relative Frequency
------------------------------------------------
1 | 0.02
2 | 0.49
3 | 0.73
4 | 0.92
5 | 1.00