Math Problem Statement

A magazine identified the following five 'maintenance' activities often performed by people as summer approaches: 1. Prep the car for road trips, 2. Clean up the house or apartment, 3. Groom the garden, 4. Exercise the body, 5. Organize the wardrobe. The following data are the responses of 30 people who were asked, on June 1st, how many of the five they had accomplished. Construct a frequency and relative frequency distribution, and select the correct histogram to represent the data.

Solution

In the image, the problem involves summarizing and visualizing data about maintenance activities commonly done at the start of summer. Here's a breakdown of the problem:

  1. Frequency Table: The table displays the frequency and relative frequency of people who completed 0 to 5 maintenance tasks. For 30 respondents, the data is summarized as follows:

    Number xxFrequency ffRelative Frequency fn\frac{f}{n}
    0620%
    1517%
    2517%
    3620%
    4413%
    5413%

    The relative frequencies are rounded to the nearest integer percentage and sum up to approximately 100%.

  2. Histogram Selection: The question asks to choose the correct histogram based on the frequency data provided. Observing the frequency values for each activity count (0 to 5), the correct histogram should show:

    • Highest bars at 0 and 3 (frequency of 6 each),
    • Moderate bars at 1 and 2 (frequency of 5 each),
    • Lower bars at 4 and 5 (frequency of 4 each).

    Based on this, Option A seems to best match the frequencies given in the table.

Would you like further details on interpreting this data or creating the histogram?

Related Questions

  1. How do you calculate relative frequency from raw frequency?
  2. What are some common uses of histograms in data analysis?
  3. Why is it important to round relative frequencies to the nearest integer?
  4. What other types of charts could represent this data effectively?
  5. How could this data be used to make decisions about seasonal tasks?

Tip

For constructing histograms, make sure each bar accurately represents the frequency for each category to avoid misinterpretation.

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Math Problem Analysis

Mathematical Concepts

Statistics
Frequency Distribution
Relative Frequency
Data Visualization

Formulas

Relative Frequency = (Frequency / Total Number of Observations) x 100%

Theorems

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Suitable Grade Level

Grades 9-12