Question

Find the range, mean, and standard deviation of the data set (3, 6, 9, 11, 15, 16) The range is 13 (Type a whole number.) The mean is 10 (Type an integer or decimal.) The standard deviation is (Do not round until the final-answer. Then round to two decimal places as needed.) Enter your answer in the answer box and then click Check Answer All parts showing

Answer 1

Answer: The range is 13.  The mean is 10. The standard deviation is 4.62 .

Step-by-step explanation:

The given data : 3, 6, 9, 11, 15, 16

Total number of data values : n = 6

The mean of data is given by :-

$\overline{x}=\dfrac{\sum^6_{i=1}x_i}{n}\\\\\Rightarrow\overline{x}=\dfrac{60}{6}=10$

The standard deviation is given by :-

$\sqrt{\dfrac{1}{n}(\sum^6_{i=1}(x_i-\overline{x})^2)}\\\\=\sqrt{\dfrac{1}{6}(\sum^6_{i=1}(x_i-10)^2)}\\\\=\sqrt{\dfrac{1}{6}\times(49+16+1+1+25+36)}=4.61880215352\approx4.62$

The range of the data : Maximum value -Minimum value

$=16-3=13$