My question you did not calculate for the modal and the median

Mathematics

ScanSolve AI Answer

Answer

30-39\text{30-39}

33.83\text{33.83}

Step-by-step solution

8 steps

Let's calculate the modal class and the median using the provided data.

First, here is the data table again:

Age GroupFrequency (ff)Class Midpoint (xx)Cumulative Frequency (cfcf)
10-19614.56
20-291224.518
30-391534.533
40-49944.542
50-59554.547
60-69264.549
Total∑f=49\sum f = 49

2) Calculate the modal class.

  1. Identify the highest frequency in the table.

    The highest frequency is 15.

  2. Determine the class interval corresponding to the highest frequency.

    The frequency of 15 corresponds to the age group 30-39.

    The modal class is 30-39\boxed{\text{30-39}}.

    3) Calculate the median.

  3. Find the total number of observations (NN).

    N=∑f=49N = \sum f = 49
  4. Determine the position of the median.

    Median position=N2=492=24.5\text{Median position} = \frac{N}{2} = \frac{49}{2} = 24.5
  5. Identify the median class.

    The median class is the first class whose cumulative frequency (cfcf) is greater than or equal to the median position (24.5).
    From the table, the cfcf for 20-29 is 18, and for 30-39 is 33. Since 33 is the first cfcf greater than or equal to 24.5, the median class is 30-39.

  6. Identify the values for the median formula.

    • Lower boundary of the median class (LL): 30−0.5=29.530 - 0.5 = 29.5
    • Total frequency (NN): 49
    • Cumulative frequency of the class before the median class (CFCF): 18 (for 20-29)
    • Frequency of the median class (ff): 15 (for 30-39)
    • Class width (hh): 19−10+1=1019 - 10 + 1 = 10 (or 29.5−19.5=1029.5 - 19.5 = 10)
  7. Apply the median formula for grouped data.

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

    Median=29.5+(24.5−1815)×10\text{Median} = 29.5 + \left( \frac{24.5 - 18}{15} \right) \times 10 Median=29.5+(6.515)×10\text{Median} = 29.5 + \left( \frac{6.5}{15} \right) \times 10 Median=29.5+(0.4333...)×10\text{Median} = 29.5 + (0.4333...) \times 10 Median=29.5+4.333...\text{Median} = 29.5 + 4.333... Median=33.83\text{Median} = 33.83

    The median is 33.83\boxed{\text{33.83}}.

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