he numbers of participants in various library programs are shown below.
45, 34, 49, 63, 31, 30, 46, 53, 46, 51, 61, 33, 62, 40
Which histogram represents the data correctly?
A.
The histogram has a bar between 30 and 40 is raised to 5, a bar between 40 and 50 is raised to 4, a bar between 50 and 60 is raised to 3, and a bar between 60 and 70 is raised to 2.
B.
The histogram has a bar between 30 and 40 is raised to 4, a bar between 40 and 50 is raised to 5, a bar between 50 and 60 is raised to 2, and a bar between 60 and 70 is raised to 3.
C.
The histogram has a bar between 30 and 40 is raised to 2, a bar between 40 and 50 is raised to 4, a bar between 50 and 60 is raised to 5, and a bar between 60 and 70 is raised to 3.
D.
The histogram has a bar between 30 and 40 is raised to 2, a bar between 40 and 50 is raised to 3, a bar between 50 and 60 is raised to 4, and a bar between 60 and 70 is raised to 5.
The correct histogram representation of the data is:
D. The histogram has a bar between 30 and 40 raised to 2, a bar between 40 and 50 raised to 3, a bar between 50 and 60 raised to 4, and a bar between 60 and 70 raised to 5.
To determine which histogram represents the data correctly, we need to count the number of data points within each range and compare them to the heights of the bars in the histograms.
Given the data points: 45, 34, 49, 63, 31, 30, 46, 53, 46, 51, 61, 33, 62, 40
Let's analyze each option:
A.
The histogram has a bar between 30 and 40 raised to 5.
The histogram has a bar between 40 and 50 raised to 4.
The histogram has a bar between 50 and 60 raised to 3.
The histogram has a bar between 60 and 70 raised to 2.
B.
The histogram has a bar between 30 and 40 raised to 4.
The histogram has a bar between 40 and 50 raised to 5.
The histogram has a bar between 50 and 60 raised to 2.
The histogram has a bar between 60 and 70 raised to 3.
C.
The histogram has a bar between 30 and 40 raised to 2.
The histogram has a bar between 40 and 50 raised to 4.
The histogram has a bar between 50 and 60 raised to 5.
The histogram has a bar between 60 and 70 raised to 3.
D.
The histogram has a bar between 30 and 40 raised to 2.
The histogram has a bar between 40 and 50 raised to 3.
The histogram has a bar between 50 and 60 raised to 4.
The histogram has a bar between 60 and 70 raised to 5.
Now, let's compare the counts to the heights of the bars in each histogram:
Option A: The count of data points between 30 and 40 is 2, not 5. Incorrect.
Option B: The count of data points between 30 and 40 is 2, not 4. Incorrect.
Option C: The count of data points between 30 and 40 is 2, correct. The count of data points between 40 and 50 is 4, correct. The count of data points between 50 and 60 is 4, not 5. Incorrect.
Option D: The count of data points between 30 and 40 is 2, correct. The count of data points between 40 and 50 is 4, correct. The count of data points between 50 and 60 is 4, correct. The count of data points between 60 and 70 is 3, not 5. Incorrect.
Based on the analysis, the histogram that represents the data correctly is option D, where the bars represent the counts of data points in each range accurately.
To determine which histogram represents the data correctly, we need to analyze the given numbers and construct a histogram based on the frequency of the values within specific ranges.
Here are the steps to construct the correct histogram:
1. Count the frequency of each value within the given data.
45: 2
34: 1
49: 1
63: 1
31: 1
30: 2
46: 2
53: 1
51: 1
61: 1
33: 1
62: 1
40: 1
2. Determine the ranges and their frequencies:
Range 30-40: 2 (30, 40)
Range 40-50: 4 (45, 46, 49, 40)
Range 50-60: 3 (53, 51, 53)
Range 60-70: 2 (63, 62)
3. Compare the constructed histogram with each option:
A. 5, 4, 3, 2 - Does not match the frequencies.
B. 4, 5, 2, 3 - Matches the frequencies.
C. 2, 4, 5, 3 - Does not match the frequencies.
D. 2, 3, 4, 5 - Does not match the frequencies.
Based on the analysis, option B, which has a bar between 30 and 40 raised to 4, a bar between 40 and 50 raised to 5, a bar between 50 and 60 raised to 2, and a bar between 60 and 70 raised to 3, represents the data correctly