Question

model it: data descriptions

try these two problems about describing data distributions.

2 a. mr. abas students do a math puzzle. use the
dot plot to complete the frequency table.

b. the data for mr. abas class are spread from
a fastest time of _ minutes to a slowest time of _ minutes.
4 when you describe how spread out data values are, you are describing
the variability of the data set. the range of a data set describes the
variability by telling how far apart the greatest and least data values are.
the range of the data for mr abas class is _ minutes.

Explanation:

Step1: Analyze the dot - plot for frequency

The number of dots above a value on the dot - plot represents its frequency.

• For \(7\) minutes: There are \(2\) dots.
• For \(8\) minutes: Count the dots. There are \(3\) dots.
• For \(9\) minutes: Count the dots. There are \(3\) dots.
• For \(10\) minutes: Count the dots. There are \(4\) dots.
• For \(11\) minutes: Count the dots. There are \(3\) dots.
• For \(12\) minutes: There are \(2\) dots.

Step2: Find the fastest and slowest times

The left - most value on the dot - plot is the fastest time. The left - most non - zero number of dots is at \(7\) minutes.
The right - most value on the dot - plot is the slowest time. The right - most non - zero number of dots is at \(12\) minutes.

Step3: Calculate the range

The formula for the range \(R\) of a data set is \(R=\text{Max}-\text{Min}\), where \(\text{Max}\) is the maximum value and \(\text{Min}\) is the minimum value.
Here, \(\text{Max} = 12\) and \(\text{Min}=7\). So \(R=12 - 7=5\)

Answer:

a.

Minutes	Frequency
\(8\)	\(3\)
\(9\)	\(3\)
\(10\)	\(4\)
\(11\)	\(3\)
\(12\)	\(2\)

b. The data for Mr. Aba's class are spread from a fastest time of \(7\) minutes to a slowest time of \(12\) minutes.

The range of the data for Mr Aba's class is \(5\) minutes.