Measures of dispersion variance standard deviation and mean deviation - One Line Questions
1.
The coefficient of variation is calculated as: —
(Standard Deviation / Mean) * 100
2.
For a sample of size n, the unbiased sample variance (s^2) is often calculated as: —
\(\frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2\)
3.
The formula for mean deviation from the mean (MD) for a dataset x1, x2, ..., xn with mean \(\bar{x}\) is: —
\(\frac{1}{n} \sum_{i=1}^{n} |x_i - \bar{x}|\)
4.
For a dataset with observations x1, x2, ..., xn and mean \(\bar{x}\), the formula for variance (\(\sigma^2\)) is: —
\(\frac{1}{n} \sum_{i=1}^{n} (x_i - \bar{x})^2\)
5.
For a continuous random variable X, the variance is given by: —
\(\int_{-\infty}^{\infty} (x - \mu)^2 f(x) dx\)
6.
The formula for variance of a discrete random variable X with probability mass function P(X=xi) is: —
\(E[(X - E[X])^2]\)
7.
What is the variance of the dataset {2, 2, 2, 2}? —
0
8.
The standard deviation of a dataset {3, 3, 3, 3, 3} is: —
0
9.
For a dataset {1, 3, 5, 7, 9}, calculate the mean deviation from the mean. —
2.0
10.
For a dataset {10, 20, 30, 40, 50}, what is the mean deviation from the mean? —
12
11.
For the dataset {10, 20, 30, 40, 50}, what is the variance? —
200
12.
If the variance of a dataset is 16, what is its standard deviation? —
4
13.
What is the standard deviation for the dataset {1, 3, 5, 7, 9}? —
\(\sqrt{8}\)
14.
If a dataset has a mean of 25 and a variance of 9, what is its standard deviation? —
3
15.
For the dataset {1, 3, 5, 7, 9}, what is the variance? —
8
16.
If the standard deviation of a dataset is 5, what is its variance? —
25
17.
If a dataset has a mean of 50 and a variance of 100, what is its standard deviation? —
10
18.
If the mean of a dataset is 10 and the standard deviation is 0, what can be concluded about the data? —
All values are 10
19.
Mean deviation is also known as: —
Average Absolute Deviation
20.
For a symmetric distribution, the mean deviation from the mean and the standard deviation are: —
Standard deviation is always greater than mean deviation
21.
If a constant 'c' is added to every observation in a dataset, how does the standard deviation change? —
It remains unchanged
22.
What is the primary disadvantage of using variance as a measure of dispersion? —
Its units are squared, making interpretation difficult
23.
If every observation in a dataset is multiplied by a constant 'k' (where k > 0), how does the standard deviation change? —
It is multiplied by k
24.
What is the square root of the variance called? —
Standard Deviation
25.
The formula \(E[X^2] - (E[X])^2\) is equivalent to: —
Variance
26.
Which measure of dispersion is most sensitive to outliers? —
Range
27.
Which of the following statements about measures of dispersion is TRUE? —
Variance is the square of standard deviation.
28.
If two datasets have the same mean, the one with the smaller standard deviation is considered: —
Less dispersed
29.
Variance is always: —
Zero or positive
30.
Which of the following properties does variance NOT possess? —
Homogeneity of degree 2
31.
The term '\(\sigma\)' typically represents: —
Population Standard Deviation
32.
The term 's' typically represents: —
Sample Standard Deviation
33.
Which measure of dispersion is sensitive to every value in the dataset? —
All of the above
34.
Which measure of dispersion is least affected by extreme values? —
Interquartile Range
35.
Which measure of dispersion is based on the difference between the first and third quartiles? —
Interquartile Range
36.
Which measure of dispersion is defined as \(\frac{Q_3 - Q_1}{2}\)? —
Quartile Deviation
37.
What is the unit of standard deviation compared to the unit of the data? —
Same
38.
The mean deviation is calculated using the: —
Absolute differences from the mean
39.
Mean deviation from the median is calculated using: —
Absolute differences from the median
40.
Which measure of dispersion is the average of the squared differences from the mean? —
Variance
41.
If mean deviation is calculated using the median, it is called: —
Median Absolute Deviation (MAD)
42.
Which of the following is a common way to calculate standard deviation for grouped data? —
Square root of the sum of (frequency * (midpoint - mean)^2) divided by the total frequency
43.
Which of the following best describes the standard deviation? —
A measure of the spread of data around the mean.
44.
In the context of probability distributions, the variance measures: —
The spread or dispersion of the random variable around its expected value
45.
Mean deviation is generally preferred over standard deviation when: —
A simpler interpretation is needed
46.
If the variance of a dataset is 0, it implies: —
All data points are identical
47.
If all values in a dataset are the same, what is the variance? —
Zero
48.
Which measure of dispersion considers the absolute differences from the mean? —
Mean Deviation
49.
Which of the following is NOT a measure of dispersion? —
Arithmetic Mean
50.
Which measure of dispersion is calculated as the difference between the largest and smallest values? —
Range