Elements of Statistics Important Question Answer For BCA 3rd Semester


Elements of Statistics Important Question Answer For BCA 3rd Semester

Elements of Statistics Important Question Answer For BCA 3rd Semester:-

(Section – A)

Very Short Question

1) Define Permutation and Combination?

Permutation: The Word permutation means only the base in which a set of objects can be arranged.

_{n} P_{r}=\frac{n !}{(n-r) !}

_{n} P_{r} = permutation

n = total number of objects

r = number of objects selected

Combination: The selection of the management of the object is called combination.

for example. 

ABC and BCA are the same combinations. the total no of combinations of ‘r’ objects select from n denoted by

_n C_r=\frac{n !}{r ! (n-r) !}

_n C_r = number of combinations

n = total number of objects in the set

r = number of choosing objects from the set

2) Define histogram.

Histogram: A histogram is a graphical display of data using bars of different sizes.

  • made for continuous data series.
  • no space between the bars. or all the bars touches each other.
  • Hegith the bars represent class interval and hence it changes as and when the class interval changes.

3) Differentiate between process and product control.

Process Control: It is concerned with controlling the quality of the product during the production process. It ensures that a product of only standard in produce and makes use of control charts.

Product Control: It is concerned with controlling the quality of the product by critical examination at strategic points. it is the product to a certain whether at makes use of sampling inspection to achieve the objectives.

Difference between process and product control

Process Control

Product Control

Process control is applied during production process. Product Control is applied after production process.
Process control is of two types: online quality control and offline quality control. Product control is no type.
Process control is an integral part of manufacturing. Product control focus on sorting and isolating defective products.
Process control is to reduce waste, minimize costs and reduce the environmental impact. In product control efforts are made to segregate and sort defective products and give signals for improving quality in process of manufacturing.
In process control the end products may be or may not be fulfilling the desired quality and costs. In product control, the end product of product control should fulfill the desired quality, control and property.

4) Define discrete and continuous variables.

Discrete Variable:

  • Countable
  • Nothing in between them
  • Infinite but countable
  • Take value in whole no.

Continuous Variable:

  • Measurable
  • Something in between them.
  • Infinite
  • Take values that are fractional & with interval.

Example are:



No. of Student Temperature
Books in Library Weight
Purchasing ticket Time, Height
Money Distance, Length

5) Define partition value.

Partition value: The Partition Values are the measures used to divide the total number of observations from a distribution into a certain number of equal parts. Quartiles, Deciles, and Percentiles are some of the most often used partition values.

6) Define classical definition of probability?

Definition: The probability of an event is the ratio of the number of cases m favorable for the evet to the number of total outcomes n(s) possible in an equiprobable sample space.

P(A) = f / N

7) What is the geometric mean along with its merits and demerits?

Geometric Mean: In Mathematics, the Geometric Mean (GM) is the average value or mean which signifies the central tendency of the set of numbers by finding the product of their values. Basically, we multiply the numbers altogether and take the nth root of the multiplied numbers, where n is the total number of data values.

Merits of Geometric Mean

  • It is rigidly defined
  • it is based upon all the observations.
  • it is suitable for further mathematical treatment.
  • it is less affected by sampling fluctuation.

Demerits of Geometric Mean

  • It is not easy to understand.
  • if any observation is zero or negative GM cannot be calculated.

(Section – B)

Short Question

1) Define –

  • Addition theorem of probability
  • Multiplication theorem probability

2) What do you mean by classification and tabulation?

3) Difference between absolute & relative measure.

4) What is the criteria of good measure of central tendency?

5) Define frequency polygon and frequency curve.

Frequency Polygon.

A frequency polygon is obtained by using the midpoints of histogram using straight lines.

  • Can also be made without drawing histogram.
  • Strait line (using scale to connect two point).

Frequency Curve.

A frequency curve is obtained by making a free-hand curve joint the midpoint of histogram.

  • Rounded line (free hand curve)

6) Differentiate between the concept of populations and samples.

7) Difference between defects and defective.

 (Section – C)

Long Question

1), What is the statistics? Scope of statistics. Limitations of statistics.

2), What do you mean by Statistical Quality Control? Explain the types of charts.

3), Discuss the various types of classification and tabulation of data in details.

4), Explain Arithmetic, Harmonic and geometric mean for grouped and ungrouped data with their limitations.

5), Find the Mean, Median, Mode wage of the following distribution.

Wages (In Rs.) No. of Labors.
20-30 3
30-40 5
40-50 20
50-60 10
60-70 5


6), Define median and Quartiles. Explain their uses. Calculate first and third quartiles of the following data:

Wages (In Rs.) No. of Labors
60-70 5
50-60 10
40-50 20
30-40 5
20-30 2


7), Discuss additive theorem of probability. A ball is drawn at random from a box containing 6 red balls, 4 white balls and 5 blue balls. Determine the probability that it is:

  1. i) Red ii) white           iii) Blue
  2. iv) Not Red v) Red or White

8), Define mutually exclusive events and independent events

9), From a group of 3 Indians, 4 Pakistani, and 5 Americans a subcommittee of four people is selected at random. Find the probability that the sub-committee will consist of.

a), 2 Indians and 2 Pakistanis

b), 1 Indian, 1 Pakistanis and 2 Americans

10), Explain –

  • Mutually exclusive events
  • Exhaustive events
  • Independent events

11), what is the concept of dispersion? Explain in details.

12), what is the concept of measure of central tendency?

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