MathematicsOn the sports day of a school, 300 students participated. Their ages are given in the following distribution:Find the mean and mode of the data.

On the sports day of a school, 300 students participated. Their ages are given in the following distribution:


Find the mean and mode of the data.


  1. A
    11.72 years and 11.25 years
  2. B
    10.66 years and 11.95 years
  3. C
    10.95 years and 11.66 years
  4. D
    11.66 years and 10.95 years 

    Fill Out the Form for Expert Academic Guidance!l



    +91



    Live ClassesBooksTest SeriesSelf Learning



    Verify OTP Code (required)

    I agree to the terms and conditions and privacy policy.

    Solution:

    The following data is given:
    We know that the mean is given as,
    Mean=a+= 1nfiui= 1nfi×h
    In the formula, A is the  assumed mean, f is the frequency of ith class, X-is the deviation of ith  class, xi = class mark = (Upper class limit + lower class limit2, ui=xi-Ah  , fi=N= Total number of observations.
    And the mode is given as,
    Mode=l+f1 - f02f1 - f0 - f2×h
    In the formula, l will be the lower limit of  modal class. h will be the size of  class intervals. f0 will be frequency of modal class, f1  will be frequency of preceding modal class, f2  will be the frequency of succeeding modal class.
    Consider the following table:
    The mean of the data with a=12, h=12 and maximum frequency 95 will be,
    Mean=a+= 1nfiui= 1nfi×h
    Mean=12+-201300×2
    Mean=10.66 years
    Now, from the above table modal class =11-13 as the maximum frequency is 95.
    So, l=11, f0=41, f1=95,f2=36 and h=2.
    Mode=l+f1 - f02f1 - f0 - f2×h
    Mode=11+95 - 41190 - 41- 36×2
    Mode=11.95 years The mean and mode of the data is 10.66 years and 11.96 years respectively.
    Hence, option 2 is correct.
     
    Chat on WhatsApp Call Infinity Learn

      Talk to our academic expert!



      +91


      Live ClassesBooksTest SeriesSelf Learning




      Verify OTP Code (required)

      I agree to the terms and conditions and privacy policy.