Solution Found!
The following data are the measures of the diameters of 36
Chapter 2, Problem 1.22(choose chapter or problem)
The following data are the measures of the diameters of 36 rivet heads in 1/100 of an inch.
\(\begin{array}{llllllll}
6.72 & 6.77 & 6.82 & 6.70 & 6.78 & 6.70 & 6.62 & 6.75 \\
6.66 & 6.66 & 6.64 & 6.76 & 6.73 & 6.80 & 6.72 & 6.76 \\
6.76 & 6.68 & 6.66 & 6.62 & 6.72 & 6.76 & 6.70 & 6.78 \\
6.76 & 6.67 & 6.70 & 6.72 & 6.74 & 6.81 & 6.79 & 6.78 \\
6.66 & 6.76 & 6.76 & 6.72 & & & &
\end{array}\)
(a) Compute the sample mean and sample standard deviation.
(b) Construct a relative frequency histogram of the data.
(c) Comment on whether or not there is any clear indication that the sample came from a population that has a bell-shaped distribution.
Questions & Answers
QUESTION:
The following data are the measures of the diameters of 36 rivet heads in 1/100 of an inch.
\(\begin{array}{llllllll}
6.72 & 6.77 & 6.82 & 6.70 & 6.78 & 6.70 & 6.62 & 6.75 \\
6.66 & 6.66 & 6.64 & 6.76 & 6.73 & 6.80 & 6.72 & 6.76 \\
6.76 & 6.68 & 6.66 & 6.62 & 6.72 & 6.76 & 6.70 & 6.78 \\
6.76 & 6.67 & 6.70 & 6.72 & 6.74 & 6.81 & 6.79 & 6.78 \\
6.66 & 6.76 & 6.76 & 6.72 & & & &
\end{array}\)
(a) Compute the sample mean and sample standard deviation.
(b) Construct a relative frequency histogram of the data.
(c) Comment on whether or not there is any clear indication that the sample came from a population that has a bell-shaped distribution.
ANSWER:Step 1 of 4
(a) According to the definition of the sample mean, we get:
\(\begin{array}{l} \bar{x}=\sum_{i=1}^{n} \frac{x_{i}}{n} \\ =\frac{6.72+6.77+6.82+\ldots+6.76+6.72}{36} \\ =\frac{242.1396}{36} \\ =6.7261 \end{array}\)
So, the sample mean is \(\bar{x}=6.7261\)