Math Problem Statement

help solve the blanks

help solve the blanks

Solution

From the data shown in the image, let's construct the frequency (ff) and relative frequency (fn\frac{f}{n}) distributions step-by-step.


Step 1: Identify the Data Set

The dataset provided in the table is: 0,4,1,0,3,1,0,2,5,0,1,4,3,1,0,2,4,0,3,1,0,2,4,0,3,1,0,2,3,2.0, 4, 1, 0, 3, 1, 0, 2, 5, 0, 1, 4, 3, 1, 0, 2, 4, 0, 3, 1, 0, 2, 4, 0, 3, 1, 0, 2, 3, 2.

Step 2: Calculate Frequency (ff)

Count how many times each number occurs:

  • x=0x = 0: Appears 77 times.
  • x=1x = 1: Appears 66 times.
  • x=2x = 2: Appears 66 times.
  • x=3x = 3: Appears 66 times.
  • x=4x = 4: Appears 44 times.
  • x=5x = 5: Appears 11 time.

So, the frequencies are: f={7,6,6,6,4,1}.f = \{7, 6, 6, 6, 4, 1\}.


Step 3: Calculate Relative Frequency (fn\frac{f}{n})

The relative frequency is the frequency divided by the total number of observations (n=30n = 30): fn=frequencytotal responses.\frac{f}{n} = \frac{\text{frequency}}{\text{total responses}}.

  • For x=0x = 0: 730=0.233\frac{7}{30} = 0.233 (23.3%).
  • For x=1x = 1: 630=0.200\frac{6}{30} = 0.200 (20.0%).
  • For x=2x = 2: 630=0.200\frac{6}{30} = 0.200 (20.0%).
  • For x=3x = 3: 630=0.200\frac{6}{30} = 0.200 (20.0%).
  • For x=4x = 4: 430=0.133\frac{4}{30} = 0.133 (13.3%).
  • For x=5x = 5: 130=0.033\frac{1}{30} = 0.033 (3.3%).

Final Table:

Number xxFrequency ffRelative Frequency fn\frac{f}{n}
0723.3%
1620.0%
2620.0%
3620.0%
4413.3%
513.3%

Would you like me to assist with parts (b) or (c) from the problem? Let me know!


Related Questions:

  1. How can this data be represented using a pie chart?
  2. What is the cumulative frequency distribution for these responses?
  3. What is the median number of activities completed by the respondents?
  4. How can this data be used to calculate the mean number of activities completed?
  5. What is the variance and standard deviation for this dataset?

Tip:

To double-check frequency counts, ensure that the total of all frequencies equals the total dataset size (n=30n = 30).

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Math Problem Analysis

Mathematical Concepts

Frequency Distribution
Relative Frequency
Statistics

Formulas

Relative Frequency = Frequency / Total Observations
Sum of all Frequencies = Total Observations

Theorems

Basic Frequency Distribution and Relative Frequency Calculation

Suitable Grade Level

Grades 6-9