Question

here are the foot lengths (in centimeters) for a random sample of seven 14 - year - olds from the united kingdom. 25 22 20 25 24 24 28 calculate the standard deviation. $s_{x}=square$ centimeters (round to 2 decimal places.) interpret the standard deviation. in each interpretation, $s_{x}$ represents the value of the standard deviation. on average, the foot length of every 14 - year - old from the united kingdom was at least $s_{x}$ cm away from every other 14 - year - olds foot length. the foot length of a 14 - year - olds from the united kingdom varies from the median by about $s_{x}$ cm, on average. on average, the foot length of each 14 - year - old from the united kingdom is at least $s_{x}$ standard deviations above the third quartile or below the first quartile. the foot length for a random sample of seven 14 - year - olds from the united kingdom typically varies from the mean by about $s_{x}$ cm.

Explanation:

Step1: Calculate the mean

The data set is \(25, 22, 20, 25, 24, 24, 28\). The mean \(\bar{x}=\frac{25 + 22+20 + 25+24+24+28}{7}=\frac{168}{7} = 24\).

Step2: Calculate the squared - differences

\((25 - 24)^2=1\), \((22 - 24)^2 = 4\), \((20 - 24)^2=16\), \((25 - 24)^2 = 1\), \((24 - 24)^2=0\), \((24 - 24)^2=0\), \((28 - 24)^2 = 16\).

Step3: Calculate the variance

The variance \(s^{2}=\frac{1+4 + 16+1+0+0+16}{7 - 1}=\frac{38}{6}\approx6.33\).

Step4: Calculate the standard deviation

The standard deviation \(s=\sqrt{s^{2}}=\sqrt{\frac{38}{6}}\approx2.52\).

Answer:

\(2.52\)

The correct interpretation of the standard deviation is: The foot - length for a random sample of seven 14 - year - olds from the United Kingdom typically varies from the mean by about \(s_{x}\) cm.