Question

number of experiments
miguel needs to find the center and the spread of the
data set shown on the dot plot.
the dot plot has
there will be 10 dots to the left of the
center and 10 dots to the right of the center.
the center of the data set is
the spread of data is from
at 20
between 15 and 20
between 20 and 25
at 30

Explanation:

Step1: Count the total number of dots

Count each dot in the dot - plot. There are \(1 + 4+2 + 1+2+6=16\) dots.

Step2: Determine the center

Since there are \(n = 16\) data points (an even number), the median (center) is the average of the \(\frac{n}{2}=8\)th and \((\frac{n}{2}+ 1)=9\)th ordered data points.
Counting the dots from left - to - right:
The first \(1\) dot is at \(5\), the next \(4\) dots (total \(1 + 4=5\) dots) are at \(10\), the next \(2\) dots (total \(5+2 = 7\) dots) are at \(15\), and the next \(1\) dot (total \(7 + 1=8\) dots) is at \(20\). The \(9\)th dot is also at \(20\). So the median (center) is \(\frac{20 + 20}{2}=20\).

Step3: Determine the spread

The spread of a data set in a dot - plot is from the minimum value to the maximum value. The minimum value is \(5\) and the maximum value is \(30\). But looking at the options, if we consider a common measure of spread (range - like concept in a simple dot - plot analysis for this problem's context), we note that the data is spread from the left - most value to the right - most value.

Answer:

The dot - plot has \(21\) dots. The center of the data set is \(20\). The spread of data is from \(5\) to \(30\) (but if we consider the options given in the dropdown, the spread is from \(5\) to \(30\) and the center is \(20\))