Foot lengths Here are the foot lengths (in centimeters) for a random sample of seven 14-year-olds from the United Kingdom:

Calculate the standard deviation. Interpret this value.

Short Answer

Expert verified

The standard deviation is 2.5166 cm.

Step by step solution

01

Step 1. Given information.

The given random sample is:

25, 22, 20, 25, 24, 24, 28

02

Step 2. Find the mean.

x¯=i=1nxin=25+22+20+25+24+24+287=1687=24

03

Step 3. Find the standard deviation.

s2=(x-x¯)2n-1=(25-24)2+22-242+20-242+25-242+24-242+24-242+28-2427-1=1+4+16+1+0+0+166=3866.3333

The standard deviation is:

role="math" localid="1653665598603" s=s2=6.333=2.516cm

The standard deviation is roughly 2.5166 cm since the units of the standard deviation are the same as the units of the data values.

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