Question

Henry recorded the number of miles he biked each day for a week. His miles were 25, 40,35, 25, 40, 60, and 75,

Enter the data into the statistics calculator,
What is the standard deviation of the miles Henry biked to the nearest tenth?

Answer 1

17.1

Explanation:

The standard deviation of the miles Henry hiked is 17.1

Answer 2

SD = 17.1 miles

Explanation:

In order to find the SD we have to calculate mean first

So,

`Mean = (sum)/(no.\ of\ items) \\=(25+40+35+25+40+60+75)/(7)\\ =(300)/(7)\\ =42.86`

Now mean will be subtracted from each value and the answers will be squared

So,

X X-mean (X-mean)^2

25 -17.86 318.9796

40 -2.86 8.1796

35 -7.86 61.7796

25 -17.86 318.9796

40 -2.86 8.1796

60 17.14 293.7796

75 32.14 1032.9796

So,

Sum of squares = 2042.8572

As SD is the square root of variance

so,

Variance = Sum of squares / number of data values

=2042.8572/7

=291.84

Hence,

`SD = √(Variance) =√(291.84) \\=17.083\\to\ the\ nearest\ tenth\\SD=17.1\ miles` ..