question 24\nanswer to two decimal places\nfind the mode:\nfind the range:\nfind the standard…

Answer:

19, 26, 6.97

Explanation:

Step1: Find the mode

The mode is the number that appears most frequently. In the data set (18, 13, 19, 12, 27, 11, 15, 25, 19, 1), the number (19) appears twice and all other numbers appear only once.

Step2: Find the range

The range is calculated as ( \text{Range}=\text{Max}-\text{Min}). The maximum value in the data set is (27) and the minimum value is (1). So, ( \text{Range}=27 - 1=26)

Step3: Find the standard deviation

First, find the mean (\bar{x}). [ \bar{x}=\frac{18 + 13+19+12+27+11+15+25+19+1}{10}=\frac{150}{10} = 15 ] Then, use the formula for the sample standard deviation (s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}}) [ \begin{align*} \sum_{i=1}^{10}(x_{i}-\bar{x})^{2}&=(18 - 15)^{2}+(13-15)^{2}+(19 - 15)^{2}+(12-15)^{2}+(27-15)^{2}+(11 - 15)^{2}+(15-15)^{2}+(25-15)^{2}+(19-15)^{2}+(1 - 15)^{2}\ &=9+4 + 16+9+144+16+0+100+16+196\ &=510 \end{align*} ] [ s=\sqrt{\frac{510}{9}}\approx\sqrt{56.67}\approx6.97 ]