Question

Is it possible to obtain a negative value for the variance or the standard deviation? Standard...

Is it possible to obtain a negative value for the variance or the standard deviation? Standard deviation and variance are measures of distance and are always greater than or equal to zero. It is therefore not possible to obtain a negative value for the variance or the standard deviation.

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

No,  it is not possible to obtain a negative value for the variance or the standard deviation.

Variance of a random variable ( say X) is the sum of the square of diviation from a mean and then divide it by the total number of observations(say, n) .

Since the numerator of the variance is the sum of square values and denominator is the integer value, thus their division is positive or zero. Note that variance is equal to zero when all the values of a variable are same.

So that It is therefore not possible to obtain a negative value for the variance or the standard deviation.

Standard deviation is the positive square root of variance, so it is also equal to zero or greater than zero.

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Problem Set 6: a) The variance is high if the mean is a good measure for...
Problem Set 6: a) The variance is high if the mean is a good measure for central tendency. b) If the covariance of X and Y is close to −1, then there is a weak negative relationship between X and Y . c) The standard deviation of X is always greater than or equal to the variance of X. d) The covariance of X and Y is always smaller than or equal to the correlation coefficient of X and Y...
1a.Given the sample standard deviation of a data set is 10.34, what is the sample variance?...
1a.Given the sample standard deviation of a data set is 10.34, what is the sample variance? (a) 3.22 (b) 106.92 (c) 9.34 (d) 20.68 1b.Subtracting 3 from each value in a data set would not change which of the following measures? (a) The range (b) The sample variance (c) The standard deviation (d) All of the above would not change.
True or false a. The standard deviation is negative for a data set where all values...
True or false a. The standard deviation is negative for a data set where all values are negative. b. A population with an average of 20 and variance of 16, has a coefficient of variation equal to the mean. c.The standard deviation is a measure of dispersion that does not take into account all the observations of a data set. d.The route of a data set is affected by the existence of extreme values.
1) If the standard deviation is of a distribution is 10, the variance for the distribution...
1) If the standard deviation is of a distribution is 10, the variance for the distribution is A. Half the value of the standard deviation or 5 B.  The standard deviation squared or 100 2) What type of variable would represent number of pounds lost? A. Ratio. B. Interval 3) If half the variance of a distribution is 50, what is ¼ the standard deviation of the distribution? A 10. B. 2.5 4) Combined, a bat and a ball cost $1.10,...
With respect to calculating variance and standard deviation for a sample, What value will you get...
With respect to calculating variance and standard deviation for a sample, What value will you get when you sum the deviation scores (x – M)? What is typically done instead of just summing the deviation scores? If you are given the calculated variance for a distribution of scores in a sample, how would you convert this value to the standard deviation?
Calculate the mean, the variance, and the standard deviation of the following discrete probability distribution. (Negative...
Calculate the mean, the variance, and the standard deviation of the following discrete probability distribution. (Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places. Round your final answers to 2 decimal places.) x −41 −27 −8 −3 P(X = x) 0.29 0.35 0.21 0.15
Calculate the mean, the variance, and the standard deviation of the following discrete probability distribution. (Negative...
Calculate the mean, the variance, and the standard deviation of the following discrete probability distribution. (Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places. Round your final answers to 2 decimal places.) x −41 −27 −8 −3 P(X = x) 0.29 0.35 0.21 0.15
True or False: a.) Variance is the mean of the squared deviation score. b.) For any...
True or False: a.) Variance is the mean of the squared deviation score. b.) For any population, a z-score of +1.00 corresponds to a location above the mean by one standard deviation. c.) In a distribution with s=8, a score of X=64 corresponds to z=-.50. The mean for this sample will be M=60. d.) Transforming X values into z-scores will not change the shape of the distribution. e.) One advantage of transforming X values into z-scores is that the transformation...
Write the symbols of summary measures (mean, variance, and standard deviation) for both observed data and...
Write the symbols of summary measures (mean, variance, and standard deviation) for both observed data and theoretical distributions:
1. the area under the normal distribution curve that lies within one standard deviation of the...
1. the area under the normal distribution curve that lies within one standard deviation of the mean is approxiamtely ____%. 2. for a normal distribution curve with a mean of 10 and a standard deviation of 5, what is the range of the variable thay defines the area under the curve correaponding to a probability of approximately 68%? true or false: 3. a probability can be greater than one, but not equal to zero. 4. quartiles are used in box...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT