Question 17 of 21intermediate🔧 ApplyNumerical4 marks

If the median of the distribution given below is 28.5, find the values of xx and yy.

Class intervalFrequency
0 - 105
10 - 20xx
20 - 3020
30 - 4015
40 - 50yy
50 - 605

Total | 60 |

Correct Answer

x = 8 and y = 7

Exercise: EXERCISE 13.3 | Q: 2 | (Page 28)
For More Understanding

Explanation

This question is from Exercise 13.3, Question 2 of the NCERT textbook. It tests the student's understanding of the median formula for grouped data. The solution requires two steps: first, using the total frequency to establish a relationship between x and y, and second, using the median formula to find the exact values. The median class is identified as 20-30 since the median 28.5 lies in this interval.

Solution Steps

  1. Step 1: Calculate cumulative frequencies. | Class interval | Frequency | Cumulative Frequency | | 0 - 10 | 5 | 5 | | 10 - 20 | x | 5 + x | | 20 - 30 | 20 | 25 + x | | 30 - 40 | 15 | 40 + x | | 40 - 50 | y | 40 + x + y | | 50 - 60 | 5 | 45 + x + y |

  2. Step 2: Use total frequency to find relation between x and y. Given: Total = 60 So, 45 + x + y = 60 Therefore, x + y = 15 ... (1)

  3. Step 3: Identify the median class. Given: Median = 28.5 Since median 28.5 lies in class 20-30, the median class is 20-30. Here, l = 20, f = 20, cf = 5 + x, h = 10, n = 60

  4. Step 4: Apply the median formula. Median = l + [(n/2 - cf)/f] × h 28.5 = 20 + [(30 - (5 + x))/20] × 10 28.5 = 20 + [(25 - x)/20] × 10 28.5 = 20 + (25 - x)/2 8.5 = (25 - x)/2 17 = 25 - x x = 8

  5. Step 5: Find y using equation (1). From x + y = 15: 8 + y = 15 y = 7

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