# Statistical Quality Control Questions and Answers – Modeling Process Quality – Describing Variation – 2

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This set of Statistical Quality Control Questions and Answers for Experienced people focuses on “Modeling Process Quality – Describing Variation – 2”.

1. The most important measure of central tendency in a sample is _____
a) Sample Average
b) Sample variance
c) Frequency of highest observation
d) Frequency of lowest observation

Explanation: For a sample data of n observations, sample average is the most important measure of central tendency. It is arithmetic mean of all the observations of the sample data.

2. Which of these is called the center of mass of the sample data?
a) Sample variance
b) Median of the data
c) Arithmetic mean of the data
d) The number having the highest frequency

Explanation: The histogram exactly “balances” at the point of the sample average, which is arithmetic mean of the whole data. So it is called the center of mass of the data.

3. The variability in the sample data is measured by _____
a) Sample Data
b) Sample mean
c) Sample variance
d) Range of data

Explanation: The sample variance is the measure of the variability of the sample data, because it shows deviation of the observations from the mean of the data.

4. The sample mean/average of the data is expressed by _____
a) $$\sum_0^n x_i \div n$$
b) $$\sum_0^{n-1} x_i \div (n-1)$$
c) $$\sum_1^{n-1} x_i \div (n-1)$$
d) $$\sum_{i=1}^n x_i \div n$$

Explanation: The mean of a sample data with n number of observations is expressed by,
$$\overline{x} = \sum_{i=1}^n x_i \div n$$

5. Which of the expression/inequality is always true?
a) $$\overline{x} = s$$
b) sample standard deviation = $$\sqrt{Sample \,Variance}$$
c) sample standard deviation > sample variance
d) $$\overline{x} = s^2$$

Explanation: Sample variance is always the square of the sample standard deviation. This clarifies that,
sample standard deviation = $$\sqrt{Sample \,Variance}$$.

6. The standard deviation of the data is expressed by _____
a) $$s = \left\{\frac{\sum_{i=1}^n (x_i – \overline{x})^2}{n}\right\}^{1/2}$$
b) $$s = \left\{\frac{\sum_{i=1}^n (x_i – \overline{x})^2}{n-1}\right\}^{1/2}$$
c) $$s = \frac{\sum_{i=1}^n (x_i – \overline{x})^2}{n-1}$$
d) $$s = \frac{\sum_{i=1}^n (x_i – \overline{x})^2}{n}$$

Explanation: The data sample standard deviation is expressed as,
$$s = \left\{\frac{\sum_{i=1}^n (x_i – \overline{x})^2}{n-1}\right\}^{1/2}$$

7. The standard deviation does not reflect the magnitude of the sample data, only the scatter about the average.
a) True
b) False

Explanation: The standard deviation of a sample data is the square root of the sample variance. As variance is also calculated with respect to the mean, the above statement is true.

8. The sample variance is always greater than or equal to the sample standard deviation.
a) True
b) False

Explanation: Although sample variance is the square of sample standard deviation, but it can never be predicted that it will always be greater than or equal to the sample standard deviation. For example, for S.D. = 0.2, Variance = 0.04.

9. Which of these cannot be displayed by the box plot?
a) Location or central tendency
c) Departure from symmetry
d) Mean of the data

Explanation: The box plot graphically displays simultaneously several features of data, such as location, spread/variability, departure from symmetry, and identification of outliers.

10. Line at the either end of the box plot shows the _____
a) Extreme values
b) First quartile
c) Third quartile
d) Median

Explanation: A line at the either end of the box of the box plot shows the extreme values, i.e. maximum and minimum values. This line is also called whisker, bases on what, the box plot is also called box and whisker plot.

11. Probability distribution relates the value of a variable to ____
a) Its frequency
b) Its probability of occurrence
c) Random variable
d) Probability of occurrence of values other than that

Explanation: Probability distribution is a mathematical model, which relates the value of the variable with the probability of occurrence of that value in the population.

12. Which of these statements give exact definition of a random variable?
a) A random value from the set of integers
b) A random value from the set of natural numbers
c) A random value from the set of whole numbers which can take many values
d) A variable which takes on different values in population according to some random mechanism

Explanation: A random variable is generally described as a variable, which can take different values in population, i.e. the set of data, and follows no calculated mechanism.

13. Which of these gives a correct definition of continuous distributions?
a) Probability distribution of the variable being measured which takes on random values
b) Probability distribution of the variable being measured which takes on values dependent over a calculated mechanism
c) Probability distribution of the variable which takes some certain values such as integers
d) Probability distribution of the variable being measured that takes values on continuous scale

Explanation: When the parameter being measured can be expressed only on a continuous scale, its probability distribution is called a continuous distribution. E.g. length of a chip.

14. Which of these expressions is correctly describing a continuous distribution?
a) P(x=xi)=1-P(x≠xi)
b) P{a≤x≤b} = $$\int_a^b f(x)dx$$
c) P{x=xi}=p(xi)
d) P(x=xi)≤1-p(x≠xi)

Explanation: For a continuous distribution, probability of a value x lying in between a and b is expressed as,
P{a≤x≤b} = $$\int_a^b f(x)dx$$

15. Which of these give an expression for the mean of a continuous distribution?
a) $$\int_{-\infty}^{\infty} xf(x)dx$$
b) $$\sum_{i=1}^{\infty} x_i p(x_i)$$
c) $$\sum_{i=1}^{\infty} (x-\mu)^2 f(x)dx$$
d) $$\int_{-\infty}^{\infty} (x-\mu)^2 p(x_i)$$
$$\int_{-\infty}^{\infty} xf(x)dx$$