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Punjab (PTB) · Full book test · Free

1st Year Statistics Full Book Paper

75 marks · 2 hours 30 minutes · 39 questions. Covers: 9 chapters (CHAP 1: Introduction to Statistics to CHAP 9: Binomial and Hyper Geometric Probability Distribution).

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1st Year Statistics Full Book Paper

1st Year · Statistics · Punjab (PTB)

Name: ____________Roll No: ________Class/Section: ________Date: ________Total marks: 75Time: 2 hours 30 minutes

Q1. Multiple choice questions (Attempt all · 15 × 1 = 15)

  1. The number of trial in binomial distribution is:

    1. Not fixed

    2. Fixed

    3. Large

    4. Small

  2. The probability of drawing a king of spade from a pack of 52 cards is

  3. The random number o to 9 ae called random numbers:

    1. 1-digit

    2. 2-digit

    3. 3-digit

    4. 4-digit

  4. If X and Y are independent random variables, then E(XY) is equal to

    1. E(XY)

    2. E(X) E(Y)

    3. XE(Y)

    4. YE(X)

  5. Registration is the source of:

    1. Primary data

    2. Secondary data

    3. Ogive

    4. Histogram

  6. Graphs of frequency distrubutions are used because:

    1. They have a long history in practical applications

    2. They attract attention to data pattern

    3. They account for biased or incomplete data

    4. None of these

  7. Range can be calculated in open-end classes:

    1. Never

    2. Always

    3. Often

    4. Seldom

  8. The weights used in a quantity index are:

    1. Percentages of total quantity

    2. Prices

    3. Average of quantities

    4. None of these

  9. If any value in a series is zero, then we cannot calculate the:

    1. Mean

    2. Harmonic mean

    3. Mode

    4. Median

  10. The parameters of the hypergeometric distribution h(x; N, n, k) are:

    1. x, N, k

    2. N, n, k

    3. x, n, k

    4. x, N, n, k

  11. When a pair of dice is rolled, the sum of uppermost dots vary from:

    1. 0 to 10

    2. 1 to 11

    3. 2 to 19

    4. 2 to 12

  12. Probability proportional to size is abbreviated as:

    1. PPS

    2. SPP

    3. PPP

    4. PSP

  13. If X and Y are independent random variables, then Var (X - Y) is equal to

    1. Var (X) - Var (Y)

    2. Var (X) + Var (Y)

    3. E(X - Y)2

    4. E(X + Y)2

  14. A numerical characteristics of a sample is called:

    1. Statistic

    2. Parameter

    3. Variable

    4. Sample

  15. Histogram is a graph of:

    1. Frequency distribution

    2. Time series

    3. Qualitative data

    4. Ogive

Q2. Short questions (Attempt any 12 of 18 · 12 × 2 = 24)

  1. Distinguish between an unweighted index number and a weighted index number.

  2. If  and = 0 elsewhere. Find P(X < 1.2).

  3. Write down the merits/advantages of Median.

  4. Differentiate between a Variable and a Random variable.

  5. How random number can be generated?

  6. Find the probability i.e., tossing a fair coin four times there will appear 1 tail and 3 heads.

  7. Define histogram.

  8. Write the types of dispersion.

  9. What is the sample space when three distinct coins are tossed simultaneously? Also specify the event A 'exactly two heads occur'.

  10. Compute base year weighted and current year weighted index numbers for the given data: 

  11. If E(5X + 1) = 18 and E(5X + 10)2 = 530. Find Var(5X + 1).

  12. Find median for the following: 58 54 21 51 59 46 65 31 68 41 36

  13. How many significant digits are there in the following numbers? 400

  14. Make a random variable for number of heads when two coins are tossed.

  15. Is it possible to have a binomial distribution in the following case: P(X = -2)=0.1467

  16. What is a diagram?

  17. What would be the shape and name of the frequency distribution if: mean = median = mode

  18. Solve: 

Q3. Long questions (Attempt any 4 of 6 · 4 × 9 = 36)

  1. For two independent events A and B, P(A) = 0.25 and P(B) = 0.40. Find ?

  2. Define the word statistics and explain its different meanings.

  3. Construct the chain indices for the following data for price relatives for 1941 to 1944.

    Year Sugar Gur Tea Coffee
    1941 98 75 82 99
    1942 100 82 74 100
    1943 114 83 78 104
    1944 109 84 89 95

  4. There are three children in a family. Let the random variable denote the number of boys in a family. Write down the possible outcomes and the values assigned by the random variable assuming equal chances for boys and girls.

  5. Prepare a frequency distribution using the following grouping 35 - 39, 40 - 44.

  6. Four randomly selected students from a class are asked their opinion about the teaching system as satisfactory (S) or not satisfactory (NS). Let Y denote the number of students saying satisfactory. Write down the possible outcomes and the possible Y values.