Question
A student measures six of his fellow classmates. He obtains these data: 62, 72, 68, 55, 48, and 65 inches. Identify the false statement about the set of data.
1)the data set is too small to be made into a histogram
2)the data set id small enough that the individual numbers can be examined
3)the data set is not large enough for a histogram to reveal the true nature of the distribution
4)the histogram will be a repeat of the individual numbers
1)the data set is too small to be made into a histogram
2)the data set id small enough that the individual numbers can be examined
3)the data set is not large enough for a histogram to reveal the true nature of the distribution
4)the histogram will be a repeat of the individual numbers
Answers
Answered by
GPT-4o mini
To evaluate which statement is false regarding the dataset of heights measured (62, 72, 68, 55, 48, and 65 inches) with 6 data points, let's analyze each statement:
1) **The data set is too small to be made into a histogram.**
While a histogram typically benefits from a larger dataset to show trends and distributions effectively, you can technically create a histogram with any size dataset. However, the effectiveness and clarity of the histogram may be diminished with only 6 data points.
2) **The data set is small enough that the individual numbers can be examined.**
This statement is true. With only 6 data points, each individual number can be easily examined and analyzed.
3) **The data set is not large enough for a histogram to reveal the true nature of the distribution.**
This statement is also true. With only 6 data points, a histogram may not provide meaningful insights into the overall distribution.
4) **The histogram will be a repeat of the individual numbers.**
This statement is false. A histogram groups data into bins, and it represents the frequency of data points within those bins, rather than repeating individual numbers. With 6 different heights, the histogram would show how many data points fall within certain ranges rather than just listing the individual measurements.
Thus, the **false statement** is **4)** the histogram will be a repeat of the individual numbers.
1) **The data set is too small to be made into a histogram.**
While a histogram typically benefits from a larger dataset to show trends and distributions effectively, you can technically create a histogram with any size dataset. However, the effectiveness and clarity of the histogram may be diminished with only 6 data points.
2) **The data set is small enough that the individual numbers can be examined.**
This statement is true. With only 6 data points, each individual number can be easily examined and analyzed.
3) **The data set is not large enough for a histogram to reveal the true nature of the distribution.**
This statement is also true. With only 6 data points, a histogram may not provide meaningful insights into the overall distribution.
4) **The histogram will be a repeat of the individual numbers.**
This statement is false. A histogram groups data into bins, and it represents the frequency of data points within those bins, rather than repeating individual numbers. With 6 different heights, the histogram would show how many data points fall within certain ranges rather than just listing the individual measurements.
Thus, the **false statement** is **4)** the histogram will be a repeat of the individual numbers.
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