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    Stat Assignment No 1 For 2024 Batch

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    Sanskriti Jain

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    © All Rights Reserved
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    Stat Assignment No 1 For 2024 Batch

    Uploaded by

    Sanskriti Jain
    6 views2 pages

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    Stat Assignment No 1 for 2024 Batch

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    6 views2 pages

    Stat Assignment No 1 For 2024 Batch

    Uploaded by

    Sanskriti Jain

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 2

    Assignment No.

    1 for Internal Assessment


    Last Date of Submission: 1st March, 2024

    PART 1: Measures of Central Tendencies: Solve any five.


    1. For a certain frequency table of 200 days the mean was found to be 1.46, calculate the missing
    frequencies.
    a. Number of accidents: 0 1 2 3 4 5
    b. Number of days: 46 ? ? 25 10 5

    2. In a factory, there are 100 skilled, 150 semi-skilled and 250 unskilled workers. It has been observed
    that on an average a unit length of a particular fabric is woven by a skilled worker in 2 hours, by a semi-
    skilled worker in 3 hours and by an unskilled worker in 4 hours. After training of 2 years, the semi-skilled
    workers are expected to become skilled and the unskilled workers to become semi-skilled. How much
    less time will be required after 2 years of training for weaving the unit length of fabric by an average
    worker?

    3. Find the median of the following distribution and comment why is the median a more suitable measure
    of central tendency than mean in this case? Also find quartile deviation.

    Age (years) No. of persons (‘ 000 ) Age (years) No. of persons (‘ 000 )
    Below 10 2 Below 50 14
    Below 20 5 Below 60 15
    Below 30 9 Below 70 15.5
    Below 40 12 Above 70 15.6

    4. The frequency distribution of weight in grams of mangoes of a given variety is given below. Calculate
    the median and the range of weight of middle 50 percent of mangoes.

    Weight in grams No. of mangoes Weight in grams No. of mangoes


    410- 419 14 450 - 459 45
    420 - 429 20 460 - 469 18
    430 - 439 42 470 – 479 7
    440 – 449 54

    5. The median and mode of the following wage distribution are known to be Rs. 33.5 and Rs. 34
    respectively. Find the missing frequencies:

    Wages in Rs. No. of persons Wages in Rs. No. of persons


    0-10 4 40-50 ?
    10-20 16 50-60 6
    20-30 ? 60-70 4
    30-40 ?

    6. Find mode (by Grouping Methond):

    X: 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100 100-110
    F: 4 6 5 10 20 22 24 6 2 1

    PART 2: Measures of Dispersion and Skewness: Solve any two.


    7. (a) The arithmetic mean and the standard deviation of a set of 9 items are 43 and 5 respectively. If an
    item of value 63 is added to the set, find the mean and standard deviation of 10 items.
    (b) The means of two samples of sizes 50 and 100 respectively are 54.1 and 50.3 and the standard
    deviations are 8 and 7. Obtain the standard deviation of the sample of size 150 obtained by
    combining the two samples.
    8. The following data are given for two companies of the monthly wages paid to employees. Combining
    the data for groups of male and female employees, find out
    (i) Which company pays larger amount as monthly wages?
    (ii) Which company has a higher average monthly wage per employee?
    (iii) Which company has a smaller dispersion of monthly wages?

    Company A Company B
    Male Female Male Female
    No. of employees 40 10 20 30

    Mean 30 20 27 32

    Variance 8 3 12 5

    9. You are given the position in a factory before and after the settlement of an industrial dispute.
    Comment on the gains or losses from the point of view of workers and that of management.
    Before After
    No. of workers 3000 2900
    Mean wages (Rs) 220 230
    Median wages (Rs) 250 240
    Standard deviation (Rs) 30 26

    PART 3: Index Numbers: Solve any one.


    10. For the following data prove that the Fisher’s method satisfies both the time reversal and factor reversal
    test and calculate Index Number value.
    1980 1990
    Commodities
    Price Quantity Price Quantity
    A 6 50 10 56
    B 2 100 2 120
    C 4 60 6 60
    D 10 30 12 24

    11. A textile worker in the city of Mumbai earns Rs. 35,000 per month. The cost of living index for a
    particular month is given as 136. Using the following information, find out the amount of money he spent
    on house rent and clothing.

    Group Expenditure (Rs) Group Index


    Food 14,000 180
    Clothing ? 150
    Rent ? 100
    Fuel & Lighting 5600 110
    Miscellaneous 6300 80

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