Question 4 of 9intermediate🔧 ApplyNumerical4 marks

In a city 45 families were surveyed for the number of Cell phones they used. Prepare a frequency array based on their replies as recorded below.

Correct Answer

Step 1: Understanding Frequency Array A frequency array is used for classification of data for a discrete variable. Since the number of cell phones can only take whole number values (0, 1, 2, etc.), we prepare a frequency array showing frequencies corresponding to each value.

Step 2: Organising Raw Data The given data from 45 families is: Row 1: 1, 2, 2, 2, 1, 2, 1, 2, 2, 3, 3, 3, 3 Row 2: 3, 3, 2, 3, 2, 2, 6, 1, 6, 2, 1, 5, 1, 5 Row 3: 2, 4, 2, 7, 4, 2, 4, 3, 4, 2, 0, 3, 1, 4

Step 3: Counting Frequencies for Each Value

  • Families with 0 cell phones: 1
  • Families with 1 cell phone: 7
  • Families with 2 cell phones: 14
  • Families with 3 cell phones: 9
  • Families with 4 cell phones: 5
  • Families with 5 cell phones: 2
  • Families with 6 cell phones: 2
  • Families with 7 cell phones: 1

Step 4: Frequency Array Table

Number of Cell PhonesNumber of Families
01
17
214
39
45
52
62
71
Total41

This frequency array shows the distribution of cell phones among the surveyed families.

Exercise: EXERCISES | Q: 6 | (Page 17)
For More Understanding

Explanation

This question tests the student's understanding of frequency array for discrete variables. As explained in the textbook context, 'For a discrete variable, the classification of its data is known as a Frequency Array. Since a discrete variable takes values and not intermediate fractional values between two integral values, we have frequencies that correspond to each of its integral values.' The student needs to count the frequency of each distinct value (0-7 cell phones) and present it in a tabular format. The total comes to 41 families based on the data provided in the table.

Solution Steps

  1. Step 1: Identify that number of cell phones is a discrete variable, requiring a frequency array

  2. Step 2: Extract all values from the three rows of data

  3. Step 3: Count frequency of each distinct value (0 through 7)

  4. Step 4: Prepare the frequency array table with Number of Cell Phones and Number of Families columns

  5. Step 5: Verify total frequency equals total observations

PreviousNext