Question

Find the range and standard deviation. Table below gives the number of hours spent watching tv last week by sample 24 children.
1,7,2,1,4,7
3,5,10,9,1,4
3,5,8,1,1,8
5,5,6,10,10,7

Range= please enter an exact answer

standard deviation = please show your answer to 4 decimal places.
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Answer 1

Answer:

$R=9$

$s=3.0972$

Step-by-step explanation:

Range ($R$) is the highest value minus the lowest value.

The highest value in the data is 10, and the lowest value in the data is 1.

$R=10-1=9$

To find the standard deviation of a sample ($s$) without a calculator, use the sample variance formula for samples: $s^{2} =\frac{n(\Sigma{X^2})-(\Sigma{X})^2}{n(n-1)}$, where ${X}$ represents each individual value and $n$ represents the sample size.

1. Find the sum of the values.

$\Sigma{X}=1+7+2+1+4+7+3+5+10+9+1+4+3+5+8+1+1+8+5+5+6+10+10+7=123$

2. Square each value and find the sum.

$\Sigma{X}^{2}=1^{2}+7^{2}+2^{2}+1^{2}+4^{2}+7^{2}+3^{2}+5^{2}+10^{2}+9^{2}+1^{2}+4^{2}+3^{2}+5^{2}+8^{2}+1^{2}+1^{2}+8^{2}+5^{2}+5^{2}+6^{2}+10^{2}+10^{2}+7^{2}=851$

3. Substitute it into the sample variance formula.

$s^{2} =\frac{n(\Sigma{X^2})-(\Sigma{X})^2}{n(n-1)}=\frac{24(851)-(123)^2}{24(24-1)}=\frac{20424-15129}{24(23)}=\frac{5295}{552}=\frac{1765}{184}$

4. Take the square root of the sample variance to get the sample standard deviation.

$\sqrt{s^2}=\sqrt{\frac{1765}{184} }=3.097158586$

5. Round the sample standard deviation to four decimal places.

$s=3.0972$