The 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.
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.
why
A quick tally on the given data shows that there are five entries between 30-40, four between 40-50, three between 50-60, and two between 60-70 which corresponds to the histogram given in option A. It's also critical to keep in mind that the boundaries i.e., 40, 50, and 60 belong to the upper-class limit in a histogram.
Here's the breakdown:
30-40: 34, 31, 33, 30 (4 entries)
40-50: 45, 46, 46, 40 (4 entries)
50-60: 53, 51 (2 entries)
60-70: 63, 61, 62 (3 entries)
So, option A is the correct answer.
To determine which histogram represents the data correctly, we need to count the frequency of numbers within each range and compare it to the given options.
Using the provided data, we can determine the frequencies as follows:
- The range 30-40 has a frequency of 2.
- The range 40-50 has a frequency of 4.
- The range 50-60 has a frequency of 5.
- The range 60-70 has a frequency of 3.
Now let's compare these frequencies to the given options:
A. The histogram does not match the frequencies we calculated.
B. The histogram matches the frequencies we calculated.
C. The histogram does not match the frequencies we calculated.
D. The histogram does not match the frequencies we calculated.
Therefore, the correct histogram that represents the data is option B, where 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.
To determine which histogram represents the data correctly, we need to count the frequency of each number range.
Let's start by organizing the data into number ranges:
30-40: 30, 31, 33, 34
40-50: 40, 46, 46, 49
50-60: 51, 53, 61, 62
60-70: 63
Counting the frequency for each number range gives us:
30-40: 4
40-50: 4
50-60: 4
60-70: 1
Now let's compare this to the options given:
A. The histogram has a bar between 30 and 40 raised to 5, a bar between 40 and 50 raised to 4, a bar between 50 and 60 raised to 3, and a bar between 60 and 70 raised to 2.
B. The histogram 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.
C. The histogram has a bar between 30 and 40 raised to 2, a bar between 40 and 50 raised to 4, a bar between 50 and 60 raised to 5, and a bar between 60 and 70 raised to 3.
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.
Comparing the frequencies of the number ranges with the options, it can be seen that option B represents the data correctly. The frequency counts match the heights of the bars in the histogram given in option B.