Study MaterialsRD Sharma SolutionsRD Sharma Class 10 Solutions Chapter 7 Statistics Ex 7.3

RD Sharma Class 10 Solutions Chapter 7 Statistics Ex 7.3

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Question 1.
The following table gives the distribution of total household expenditure (in rupees) of manual workers in a city.

RD Sharma Class 10 Chapter 7 Statistics

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    Find the average expenditure ( in rupees ) per household.
    Solution:
    RD Sharma Class 10 Chapter 7 Statistics

     

    Question 2.
    A survey was conducted by a group of students as a part of their environment awareness programme, in which they collected the following data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house.

    Statistics Class 10 RD Sharma
    Which method did you use for finding the mean, and why ?
    Solution:
    Let assumed mean (A) = 7
    RD Sharma Class 10 Solutions Statistics

     

    Question 3.
    Consider the following distribution of daily wages of 50 workers of a factory.

    Statistics Class 10 RD Sharma
    Find the mean daily wages of the workers of the factory by using an appropriate method.
    Solution:
    RD Sharma Class 10 Solutions Statistics
    = 150 – 4.80 = 145.20
    Mean daily wages per worker = Rs. 145.20

    Question 4.
    Thirty women were examined in a hospital by a doctor and the number of heart beats per minute recorded and summarised as follows. Find the mean heart beats per minute for these women, choosing a suitable method.

    RD Sharma Class 10 Solutions Chapter 7 Statistics
    Find the mean of each of the following frequency distribution (5 – 14)
    Solution:
    RD Sharma Class 10 Solutions Chapter 15 Statistics Ex 15.3 4a
    Hence heart beats per minute = 75.9

    Question 5.
    Find the mean of each the following frequency distributions : (5 – 14)

    RD Sharma Class 10 Solutions Chapter 7 Statistics
    Solution:
    Let Assumed mean (A) =15

    RD Sharma Solutions Class 10 Chapter 7 Statistics
    Learncbse.In Class 10 Chapter 7 Statistics

    Question 6.
    Class 10 RD Sharma Solutions Chapter 7 Statistics
    Solution:
    RD Sharma Class 10 Pdf Free Download Full Book Chapter 7 Statistics

    Question 7.

    RD Sharma Class 10 Solution Chapter 7 Statistics
    Solution:
    RD Sharma Class 10 Solution Chapter 7 Statistics

    Question 8.
    RD Sharma Class 10 Pdf Ebook Chapter 7 Statistics
    Solution:
    RD Sharma Maths Class 10 Solutions Pdf Free Download Chapter 7 Statistics

    Question 9.
    RD Sharma Maths Class 10 Solutions Pdf Free Download Chapter 7 Statistics
    Solution:
    RD Sharma Class 10 Book Pdf Free Download Chapter 7 Statistics

    Question 10.
    RD Sharma Class 10 Book Pdf Free Download Chapter 7 Statistics
    Solution:
    Let assumed mean = 20
    Class 10 RD Sharma Chapter 7 Statistics

    Question 11.
    Class 10 RD Sharma Chapter 7 Statistics
    Solution:
    RD Sharma Maths Class 10 Solutions Chapter 7 Statistics

    Question 12.
    RD Sharma Maths Class 10 Solutions Chapter 7 Statistics
    Solution:
    RD Sharma 10 Class Solutions Chapter 7 Statistics
    RD Sharma 10 Class Solutions Chapter 7 Statistics

    Question 13.
    RD Sharma Class 10 Textbook PDF Chapter 7 Statistics
    Solution:
    RD Sharma Class 10 Textbook PDF Chapter 7 Statistics

    Question 14.
    Maths RD Sharma Class 10 Solutions Chapter 7 Statistics
    Solution:
    Maths RD Sharma Class 10 Solutions Chapter 7 Statistics
    10th Maths Solution Book Pdf Chapter 7 Statistics

    Question 15.
    For the following distribution, calculate mean using all suitable methods.
    RD Sharma 10 Chapter 7 Statistics
    Solution:
    Let assumed mean (A) = 12.5

    RD Sharma 10 Chapter 7 Statistics

    Question 16.
    The weekly observation on cost of living index in a certain city for the year 2004 – 2005 arc given below. Compute the weekly cost of living index.

    RD Sharma Class 10 Book Pdf Chapter 7 Statistics
    Solution:
    Let assumed mean (A)= 1650

    RD Sharma Class 10 Book Pdf Chapter 7 Statistics
    = 1650 + 13.46 = 1663.46

    Question 17.
    The following table shows the marks scored by 140 students in an examination of a certain paper:
    Solution Of RD Sharma Class 10 Chapter 7 Statistics
    Calculate the average marks by using all the three methods: direct method, assumed mean deviation and shortcut method.
    Solution:
    (i) Direct Method :
    Solution Of RD Sharma Class 10 Chapter 7 Statistics
    (ii) Shortcut Method:
    RD Sharma 10 Solutions Chapter 7 Statistics
    RD Sharma 10 Solutions Chapter 7 Statistics

    Question 18.
    The mean of the following frequency distribution is 62.8 and the sum of all the frequencies is 50. Compute the missing frequency / and (C.B.S.E. 2004)

    RD Sharma Maths Book For Class 10 Solution Chapter 7 Statistics
    Solution:
    RD Sharma Maths Book For Class 10 Solution Chapter 7 Statistics
    RD Sharma Class 10 Maths Chapter 7 Statistics

    Question 19.
    The following distribution shows the daily pocket allowance given to the children of a multistory building. The average pocket allowance is Rs. 18.00. Find out the missing frequency.

    RD Sharma Class 10 Maths Chapter 7 Statistics
    Solution:
    RD Sharma Mathematics Class 10 Pdf Download Free Chapter 7 Statistics
    ⇒ 752 + 20p = 792 + 18p
    ⇒ 20p- 18p = 792 – 752
    ⇒2p = 40
    ⇒p = \(\frac { 40 }{ 2 }\)
    Hence missing frequency = 20

    Question 20.
    If the mean of the following distribution is 27, find the value of p.
    RD Sharma Mathematics Class 10 Pdf Download Free Chapter 7 Statistics
    Solution:
    Mean = 27
    Answers Of RD Sharma Class 10 Chapter 7 Statistics
    ⇒ 27 (43 +p) = 1245 + 15p
    ⇒ 1161 + 21p = 1245 + 15p
    ⇒ 27p -15p= 1245 – 1161
    ⇒ 12p = 84
    ⇒ p = \(\frac { 84 }{ 12 }\)
    Hence p = 1

    Question 21.
    In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The following was the distribution of mangoes according to the number of boxes.

    Answers Of RD Sharma Class 10 Chapter 7 Statistics
    Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose ?
    Solution:
    We shall apply the assumed mean deviation method
    Let assumed mean (A) = 57
    We shall choose the method of assumed mean deviation :
    Class 10 RD Sharma Pdf Chapter 7 Statistics
    = 57 + 3 x \(\frac { 25 }{ 100 }\)
    = 57 + \(\frac { 3 }{ 16 }\)
    = 57 + 0.1875 = 57.1875 = 57.19

    Question 22.
    The table below shows the daily expenditure on food of 25 households in a locality
    Class 10 RD Sharma Pdf Chapter 7 Statistics
    Solution:
    Let assumed mean (A) = 225
    RD Sharma Class 10 Solutions Pdf Free Download Chapter 7 Statistics
    ∴ Mean expenditure on food = Rs. 211

    Question 23.
    To find out the concentration of S02 in the air (in parts per million, i.e., ppm), the data was collected for 30 localities in a certain city and is presented below :
    RD Sharma Class 10 Solutions Pdf Free Download Chapter 7 Statistics
    Find the mean concentration of S02 in the air.
    Solution:
    Let assumed mean (A) = 0.10
    RD Sharma Class 10 Solutions Pdf Free Download Chapter 7 Statistics
    Answers Of RD Sharma Class 10 Chapter 7 Statistics
    = 0.10 – 0.00133 = 0.09867 = 0.099 (approx)

    Question 24.
    A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days student was absent.
    Answers Of RD Sharma Class 10 Chapter 7 Statistics
    Solution:
    RD Sharma Class 10 Maths Chapter 7 Statistics
    ∴ Mean number of days a students was absent = 12.475

    Question 25.
    The following table gives the literacy rate (in percentage) of 3§ cities. Find the mean
    RD Sharma Class 10 Maths Chapter 7 Statistics
    Solution:
    RD Sharma 10 Solutions Chapter 7 Statistics
    RD Sharma Class 10 Maths Chapter 7 Statistics

    Question 26.
    The following is the cummulative frequency distribution (of less than type) of 1000 persons each of age 20 years and above. Determine the mean age.[NCERT Exemplar] RD Sharma 10 Solutions Chapter 7 Statistics
    Solution:
    First, we make the frequency distribution of the given data and then proceed to calculate mean by computing class marks (xi), ui’s and fiui‘s as follows:
    RD Sharma Class 10 Book Pdf Chapter 7 Statistics
    = 45 + 6.3 = 51.3
    Thus, the mean age is 51.3 years.

    Question 27.
    If the mean of the following frequency distribution is 18, find the missing frequency.
    10th Maths Solution Book Pdf Chapter 7 Statistics
    Solution:
    10th Maths Solution Book Pdf Chapter 7 Statistics

    Question 28.
    Find the missing frequencies in the following distribution, if the sum of the frequencies is 120 and the mean is 50.
    RD Sharma Class 10 Textbook PDF Chapter 7 Statistics
    Solution:
    RD Sharma Maths Class 10 Solutions Chapter 7 Statistics
    RD Sharma Class 10 Textbook PDF Chapter 7 Statistics
    ⇒ 4+ f2 -f1 = 0
    ⇒ -f2+ f1 = 4 ……..(ii)
    On adding Eqs. (i) and (ii), we get
    ⇒ 2f1 = 56
    ⇒ f1= 28
    Put the value of f1 in Eq. (i), we get
    f2 = 52-28
    ⇒ f2 = 24
    Hence, f1 = 28 and f2 = 24

    Question 29.
    The daily income of a sample of 50 employees are tabulated as follows:

    RD Sharma Class 10 Book Pdf Free Download Chapter 7 Statistics
    Find the mean daily income of employees. [NCERT Exemplar] Solution:
    Since, given data is not continuous, so we subtract 0.5 from the lower limit and add 0.5 in the upper limit of each class.
    Now we first, find the class mark xt of each class and then proceed as follows:

    RD Sharma Class 10 Book Pdf Free Download Chapter 7 Statistics
    ∴ Assumed mean, a = 300.5
    Class width, h = 200
    and total observation, N = 50
    By step deviation method,

    RD Sharma Class 10 Pdf Ebook Chapter 7 Statistics
    = 300.5 + 200 x \(\frac { 1 }{ 50 }\) x 14
    = 300.5 + 56 = 356.5

    RD Sharma Class 10 Solutions Chapter 7 Statistics Ex 7.3

     

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