Question

precision problems!
a group of students worked in separate teams to measure the length of an object.
here are their data:

team	length (cm)
team 2	2.75
team 3	2.80
team 4	2.77
team 5	2.60
team 6	2.65
team 7	2.68

• the average length is ______ cm.

this is the mean or average.

• subtract the highest value from the lowest value: ______ cm.

this is the range or spread.

• divide this number by 2: ______ cm.

this is the approximate ± range from the average.

• the precision of the measurement can be shown as average ± range.

the precision of the measurement was ____ ± ____ cm.

Explanation:

Step1: Calculate the average length

First, sum up all the length values: \(2.65 + 2.75 + 2.80 + 2.77 + 2.60 + 2.65 + 2.68\)
\[

$$\begin{align*} &2.65+2.75 = 5.4\\ &5.4 + 2.80 = 8.2\\ &8.2 + 2.77 = 10.97\\ &10.97 + 2.60 = 13.57\\ &13.57 + 2.65 = 16.22\\ &16.22 + 2.68 = 18.9 \end{align*}$$

\]
There are 7 teams, so the average is \(\frac{18.9}{7}=2.7\) cm.

Step2: Find the highest and lowest values

The values are \(2.65, 2.75, 2.80, 2.77, 2.60, 2.65, 2.68\). The highest value is \(2.80\) cm and the lowest is \(2.60\) cm. Subtract them: \(2.80 - 2.60 = 0.20\) cm.

Step3: Divide the range by 2

The range is \(0.20\) cm, so dividing by 2 gives \(\frac{0.20}{2}=0.10\) cm.

Step4: Express as average ± range/2

The average is \(2.7\) cm and the range from the average (half - range) is \(0.10\) cm, so it is \(2.7\pm0.10\) cm.

Answer:

• The average length is \(\boldsymbol{2.7}\) cm.
• Subtract the highest value from the lowest value: \(\boldsymbol{0.20}\) cm.
• Divide this number by 2: \(\boldsymbol{0.10}\) cm.
• The precision of the measurement was \(\boldsymbol{2.7\pm0.10}\) cm.