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Calculate the median weight of students from the following frequency distribution table.

Mathematics

ScanSolve AI Answer

Answer

53.75 kg\text{53.75 kg}

Step-by-step solution

5 steps
  1. Calculate the cumulative frequency (cf) for the given data.

    Weight (kg)Number of students (f)Cumulative Frequency (cf)
    40-4599
    45-5059 + 5 = 14
    50-55814 + 8 = 22
    55-60922 + 9 = 31
    60-65631 + 6 = 37
    65-70337 + 3 = 40

    The total number of students, N=40N = 40.

  2. Determine the median class.

    The median position is N2=402=20\frac{N}{2} = \frac{40}{2} = 20.
    The cumulative frequency just greater than or equal to 20 is 22, which corresponds to the class interval 50-55.
    Therefore, the median class is 50-55.

  3. Identify the values for the median formula.

    From the median class 50-55:

    • Lower limit of the median class, L=50L = 50
    • Cumulative frequency of the class preceding the median class, cf=14cf = 14
    • Frequency of the median class, f=8f = 8
    • Class size, h=55−50=5h = 55 - 50 = 5
    • N2=20\frac{N}{2} = 20
  4. Apply the median formula for grouped data.

    The formula for the median is:

    Median=L+(N2−cff)×h\text{Median} = L + \left( \frac{\frac{N}{2} - cf}{f} \right) \times h
  5. Substitute the values and calculate the median.

    Median=50+(20−148)×5\text{Median} = 50 + \left( \frac{20 - 14}{8} \right) \times 5 Median=50+(68)×5\text{Median} = 50 + \left( \frac{6}{8} \right) \times 5 Median=50+(34)×5\text{Median} = 50 + \left( \frac{3}{4} \right) \times 5 Median=50+154\text{Median} = 50 + \frac{15}{4} Median=50+3.75\text{Median} = 50 + 3.75 Median=53.75\text{Median} = 53.75

    The median weight of the students is 53.75 kg\text{53.75 kg}.

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