use the appropriate formulas and methods to answer the following questions. do not use technology as an aid…

use the appropriate formulas and methods to answer the following questions. do not use technology as an aid, unless otherwise stated. consider the following sample data, which represent weights of sea mussels grown on the california coast, in grams: { 1.4, 1.5, 1.7, 2, 2.1, 2.1, 2.1, 2.1, 2.2, 2.2, 2.3, 2.3, 2.3, 2.4, 2.4, 2.5, 2.5, 2.7, 2.9 }. first, give the mean of the data set. 2.085 next, give the median of the data set.

use the appropriate formulas and methods to answer the following questions. do not use technology as an aid, unless otherwise stated. consider the following sample data, which represent weights of sea mussels grown on the california coast, in grams: { 1.4, 1.5, 1.7, 2, 2.1, 2.1, 2.1, 2.1, 2.2, 2.2, 2.3, 2.3, 2.3, 2.4, 2.4, 2.5, 2.5, 2.7, 2.9 }. first, give the mean of the data set. 2.085 next, give the median of the data set.

Answer

Explanation:

Step1: Calculate the sum of data

Add all the values in the data - set: $1.4 + 1.5+1.7 + 2+2.1+2.1+2.1+2.1+2.2+2.2+2.3+2.3+2.3+2.4+2.4+2.5+2.5+2.7+2.9$ $=(1.4 + 1.5+1.7)+(2)+(2.1\times4)+(2.2\times2)+(2.3\times3)+(2.4\times2)+(2.5\times2)+2.7+2.9$ $=4.6+2 + 8.4+4.4+6.9+4.8+5+2.7+2.9$ $=43.7$

Step2: Calculate the number of data points

Count the number of values in the data - set. There are $n = 19$ values.

Step3: Calculate the mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. $\bar{x}=\frac{43.7}{19}\approx2.3$

Step4: Find the median

Since $n = 19$ (an odd - numbered data set), the median is the $\left(\frac{n + 1}{2}\right)$-th value when the data is arranged in ascending order. $\frac{n+1}{2}=\frac{19 + 1}{2}=10$ The 10 - th value in the ordered data set ${1.4,1.5,1.7,2,2.1,2.1,2.1,2.1,2.2,2.2,2.3,2.3,2.3,2.4,2.4,2.5,2.5,2.7,2.9}$ is $2.2$.

Answer:

Mean: $2.3$ Median: $2.2$