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.
The correct histogram representation for the given data is option 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.
To correctly represent the data in a histogram, we need to count the frequencies of each range. Let's count the frequencies for each range:
30-40: 2 participants
40-50: 4 participants
50-60: 5 participants
60-70: 3 participants
Now let's check the histograms:
A. Option A has the incorrect frequencies for each range.
B. Option B has the correct frequencies for each range.
C. Option C has the frequencies in the wrong order.
D. Option D has the correct frequencies for each range, but the order is reversed.
Based on the correct frequencies, the histogram that represents the data correctly is Option B.
To create the correct histogram, we need to count the frequency of data points falling within each range and represent it with bars of the corresponding heights.
Let's count the frequencies of the data points in the given ranges:
- Range 30-40: Two data points (30, 34)
- Range 40-50: Four data points (40, 45, 46, 46)
- Range 50-60: Five data points (49, 51, 53, 61, 62)
- Range 60-70: Three data points (63)
Now, let's compare the counted frequencies to the options provided:
A. Option A has a bar between 30 and 40 raised to 5, which is incorrect because there are only two data points in that range. It also misrepresents the other ranges.
B. Option B has a bar between 40 and 50 raised to 5, which is incorrect because there are only four data points in that range. It also misrepresents the other ranges.
C. Option C has a bar between 50 and 60 raised to 5, which is correct since there are five data points in that range. It also correctly represents the other ranges.
D. Option D has a bar between 40 and 50 raised to 3, which is incorrect because there are four data points in that range. It also misrepresents the other ranges.
Therefore, the histogram that represents the data correctly is C, where the bar between 50 and 60 is raised to 5.
30 to 40 = 4
40 to 50 = 5
50 to 60 = 2
60 to 70 = 3
The correct answer is B