Question

ten used trail bikes are randomly selected from a bike shop, and the odometer reading of each (in miles) is recorded as follows.
1902 109 657 1899 782 361 216 369 229 652
send data to excel
find the range, variance, and standard deviation. round the variance to one decimal place and the standard deviation to two decimal places, if necessary.
part 1 of 3
the range is 1793 miles.
part 2 of 3
the variance is
correct answer
435,560.5
part: 2 / 3
part 3 of 3
the standard deviation is miles.

Explanation:

Step1: Calculate the mean

First, find the sum of the data: \(1902 + 109+657 + 1899+782+361+216+369+229+652=7176\)
The number of data points \(n = 10\)
The mean \(\bar{x}=\frac{7176}{10}=717.6\)

Step2: Calculate the variance

The formula for variance \(s^{2}=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}\)
\((1902 - 717.6)^{2}=(1184.4)^{2}=1402803.36\)
\((109 - 717.6)^{2}=(-608.6)^{2}=370393.96\)
\((657 - 717.6)^{2}=(-60.6)^{2}=3672.36\)
\((1899 - 717.6)^{2}=(1181.4)^{2}=1395625.96\)
\((782 - 717.6)^{2}=(64.4)^{2}=4147.36\)
\((361 - 717.6)^{2}=(-356.6)^{2}=127163.56\)
\((216 - 717.6)^{2}=(-501.6)^{2}=251602.56\)
\((369 - 717.6)^{2}=(-348.6)^{2}=121521.96\)
\((229 - 717.6)^{2}=(-488.6)^{2}=238737.96\)
\((652 - 717.6)^{2}=(-65.6)^{2}=4303.36\)

\(\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}=1402803.36+370393.96 + 3672.36+1395625.96+4147.36+127163.56+251602.56+121521.96+238737.96+4303.36=3919922.4\)

\(s^{2}=\frac{3919922.4}{9}\approx435546.9\) (rounded to one decimal place)

Step3: Calculate the standard deviation

The formula for standard deviation \(s=\sqrt{s^{2}}\)
\(s=\sqrt{435546.9}\approx660.00\) (rounded to two decimal places)

Answer:

The variance is \(435546.9\) and the standard deviation is \(660.00\)