# Statistical Quality Control Questions and Answers – Modeling Process Quality – Describing Variation – 1

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This set of Statistical Quality Control Multiple Choice Questions & Answers (MCQs) focuses on “Modeling Process Quality – Describing Variation – 1”.

1. Which of these is not a tool to describe variation in product units?
a) The box plot
b) The histogram
c) Stem-and-Leaf plot
d) Acceptance Sampling

Explanation: The box plot, the histogram, and the Stem-and-Leaf plot, all are used to illustrate variation among the product units. But, Acceptance sampling cannot be used to describe variation as; it is not a variation describing tool.

2. Descriptive statistics is used _____
a) To develop information regarding the product sample using the measured data
b) To measure the data for a sample
c) To draw conclusions about the population
d) To control the variation

Explanation: Descriptive statistics is used to show how simple graphical and numerical techniques can be used, to summarize the information about the product. The evaluation of this information is done, by using Statistical Inference.

3. Which of these shows the ordered Stem-and-Leaf Plot?
a) Stems arranged by magnitude
b) Stems not arranged by magnitude
c) Stems and the leaves, both arranged by magnitude
d) Neither stems nor leaves are arranged by magnitude

Explanation: A Stem-and-Leaf plot is said to be ordered if it has its leaves arranged by magnitude. If it has stems also arranged with leaves, it surely is the ordered Stem-and-Leaf plot.

4. The median for an odd number of observations is _________ where n is the number of observations.
a) [(n-1)/2 + 1] rank on the ascending order of observations
b) [(n+1)/2 + 1] rank on the ascending order of observations
c) Average of [(n+1) / 2] and (n/2) rank on the ascending order of observations
d) (n/2) rank on the ascending order of observations

Explanation: Median is the fiftieth percentile of the data distribution. For the odd number of observations (n), the median is [(n-1)/2 + 1] rank on the ascending order of observations. This can also be written as [(n+1)/2] rank on the ascending order of observations.

5. For even number of observations of a data distribution, what is the median?
a) [(n-1)/2 + 1] rank on the ascending order of observations
b) (n/2) rank on the ascending order of observations
c) Average of (n/2)th observation and (n/2 + 1)th observation
d) Average of [(n+1) / 2] and (n/2) rank on the ascending order of observations

Explanation: For even number of observation (n) of a data variation, the median is Average of (n/2)th observation, and (n/2 + 1)th observation. This is because median of a data distribution is the fiftieth percentile of the data distribution.

6. IQR is defined as ____________
a) difference between fourth and first quartile
b) difference between fourth and third quartile
c) difference between third and first quartile
d) difference between second and first quartile

Explanation: IQR is expanded as interquartile range. It is defined as the difference between third and first quartile. IQR = Q3-Q1; where Q1 = First Quartile; Q3 = Third Quartile.

7. In stem-and-leaf plot, the measure of variability is _____________
a) IQR
b) Mean
c) Median
d) Third quartile

Explanation: IQR is the interquartile range, which is equal to the value of difference between third and first quartile. It is used as a measure of variability, in the case of stem-and-leaf plot.

8. Which of these, does not take time order of observations into account?
a) Time series plot
b) Run chart
c) Marginal plot
d) Stem-and-leaf plot

Explanation: Although Stem-and-leaf plot is an excellent way to visually show the variability in the observations. But it does not take time order of observations into account. So, time series plot or marginal plot or run chart is used.

9. Which of these is not the name of the intervals created for the construction of the histogram?
a) Class intervals
b) Cells
c) Bins
d) Boxes

Explanation: To construct histogram for continuous data, we must divide the range of the data into intervals, which are usually called class intervals, cells, or bins.

10. For a set of data having 100 observations, how many bins must be created for satisfactory results of histogram?
a) 25
b) 10
c) 28
d) 4

Explanation: The bin number, in the case of creating a histogram, must be between 5 and 20, to give satisfactory results. If we choose no. of bins approx. equal to the square root of the number of observations, it results well. √n=√100=10

11. The histogram has the same meaning as the box plot, i.e. there are two names of same thing.
a) True
b) False

Explanation: The histogram is a plot between the frequency of an observation in a data, and the bins of data created. But, the box plot is a graphical display that simultaneously displays many features of data, like variability and departure from symmetry.

12. Relative frequency is defined as ____________
a) difference of frequency of an observation from the highest one
b) frequency of an observation
c) highest known frequency among all frequencies of the data
d) frequencies of each bin divided by the number of observations (n)

Explanation: Relative frequencies are defined as the frequencies of each bin of the histogram, divided by the total number of observations (n) in the data. They are shown on vertical scale of histogram.

13. Cumulative frequency plot is defined as ____________
a) height of each bar less than or equal to upper limit of bin
b) height of each bar more than or equal to upper limit of bin
c) height of each bar less than or equal to lower limit of bin
d) height of each bar more than or equal to upper limit of bin

Explanation: Increasing frequency plot or Cumulative frequency plot is defined as, the histogram in which, the height of each bar is less than or equal to upper limit of the bin or class interval.

14. Frequency of a bin in the histogram must be higher than 0.
a) True
b) False

Explanation: In a histogram, frequency of an observation in a particular bin, depends on the data given. It is not necessary that frequency of a bin cannot be zero.

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

Explanation: The expression for the mean of a discrete distribution is given by,
$$\sum_{i=1}^{\infty} x_i p(x_i)$$

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