Question

complete the chart to find the mean, variance and standard deviation. remember to use commas and round numbers to the nearest tenth.

x	(\bar{x})	(x - \bar{x})	((x - \bar{x})^2)
2. 340		= - 87.5		the variance is
3. 400		= - 27.5		the standard deviation is
4. 625		= 197.5		(n =)
(sum x=)	(\bar{x}=)	(sum(x - \bar{x})^2 = 54,225.0)

Explanation:

Step1: Calculate sum of \(X\) values

\(\sum X=345 + 340+400 + 625=1710\)

Step2: Calculate the mean \(\bar{X}\)

The number of data - points \(n = 4\). \(\bar{X}=\frac{\sum X}{n}=\frac{1710}{4}=427.5\)

Step3: Calculate \((x-\bar{X})^2\) for each \(x\) value

• For \(x = 345\): \((x-\bar{X})^2=(- 82.5)^2 = 6806.25\)
• For \(x = 340\): \((x-\bar{X})^2=(-87.5)^2=7656.25\)
• For \(x = 400\): \((x-\bar{X})^2=(-27.5)^2 = 756.25\)
• For \(x = 625\): \((x-\bar{X})^2=(197.5)^2=39006.25\)

Step4: Calculate the variance \(s^{2}\)

The variance \(s^{2}=\frac{\sum(x - \bar{X})^2}{n}=\frac{54225}{4}=13556.25\approx13556.3\)

Step5: Calculate the standard deviation \(s\)

The standard deviation \(s=\sqrt{s^{2}}=\sqrt{13556.25}\approx116.4\)

Answer:

\(\sum X = 1710\), \(\bar{X}=427.5\), for \(x = 345\), \((x - \bar{X})^2=6806.3\), for \(x = 340\), \((x - \bar{X})^2=7656.3\), for \(x = 400\), \((x - \bar{X})^2=756.3\), for \(x = 625\), \((x - \bar{X})^2=39006.3\), the variance is \(13556.3\), the standard deviation is \(116.4\), \(n = 4\)