Variance And Standard Deviation

Step 1: Find the variances of the two samples.
The variance of a sample is given by the formula: By applying this formula to both samples and simplifying, we find the ratio of the variances to be .
Thus, the correct answer is (1).

Step 1: Use the formula for variance.
The formula for variance is: where is the total number of frequencies, is the frequency, and is the mean of the data.
Step 2: Calculate the mean and variance.
The variance is calculated to be 1.32 using the formula. Final Answer:

Occurance	Frequency	Freq
3.5	3	10.5	-3.59	12.887	38.661
4.5	7	31.5	-2.59	6.707	46.952
5.5	22	121	121	2.528	55.609
6.5	60	390	-0.59	0.348	20.876
7.5	85	637.5	0.41	0.168	14.298
8.5	32	272	1.41	1.988	63.632
9.5	8	76	2.41	5.809	46.47
Total	217	1538.5	-	-	286.498

Step 1: Understanding the Concept:
Variance is a measure of dispersion. If every data point in a set is scaled by a constant factor , the spread of the data increases quadratically.

Step 2: Key Formula or Approach:
If , then:

Step 3: Detailed Explanation:
Given the initial variance . The constant multiplier is . Using the property: In the format of the options, this is .

Step 4: Final Answer
The new variance is .