Question 8 of 21intermediate🔧 ApplyNumerical3 marks

A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent.

Number of days0 - 66 - 1010 - 1414 - 2020 - 2828 - 3838 - 40
Number of students111074431
Correct Answer

The mean number of days a student was absent is 12.475 days.

Exercise: EXERCISE 13.1 | Q: 8 | (Page 12)
For More Understanding

Explanation

This question requires finding the mean of grouped data using the direct method. The class mark (mid-point) of each class interval is calculated first, then multiplied by the corresponding frequency. The sum of all products divided by total frequency gives the mean.

Solution Steps

  1. Step 1: Calculate class marks (x_i) for each class interval using the formula: Class mark = (Upper limit + Lower limit)/2

  2. For 0-6: x₁ = (0+6)/2 = 3; For 6-10: x₂ = (6+10)/2 = 8; For 10-14: x₃ = (10+14)/2 = 12; For 14-20: x₄ = (14+20)/2 = 17; For 20-28: x₅ = (20+28)/2 = 24; For 28-38: x₆ = (28+38)/2 = 33; For 38-40: x₇ = (38+40)/2 = 39

  3. Step 2: Calculate f_i × x_i for each class:

  4. 11×311 \times 3 = 33; 10×810 \times 8 = 80; 7×127 \times 12 = 84; 4×174 \times 17 = 68; 4×244 \times 24 = 96; 3×333 \times 33 = 99; 1×391 \times 39 = 39

  5. Step 3: Find Σf_i × x_i = 33 + 80 + 84 + 68 + 96 + 99 + 39 = 499

  6. Step 4: Find Σf_i = 11 + 10 + 7 + 4 + 4 + 3 + 1 = 40

  7. Step 5: Calculate Mean = Σf_i × x_i / Σf_i = 499/40 = 12.475 days

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