Math Problem Statement

Values Frequency 0_to_under_2 16 2_to_under_4 17 4_to_under_6 35 6_to_under_8 68

Solution

This data represents a frequency distribution where certain ranges of values correspond to specific frequencies. Here's how we can interpret it:

Values (Range)Frequency
0 to under 216
2 to under 417
4 to under 635
6 to under 868

Key points to note:

  1. Total frequency: The sum of all the frequencies is 16+17+35+68=13616 + 17 + 35 + 68 = 136.
  2. Mode: The range with the highest frequency is 6 to under 86 \text{ to under } 8, with a frequency of 68.
  3. Median: To calculate the median, we need to find the cumulative frequencies and determine where the midpoint falls.
  4. Mean: To calculate the mean, we would need to assign a representative value for each range, often the midpoint, then multiply by the frequencies and divide by the total frequency.
  5. Histogram: This data can be visualized with a histogram, showing the frequencies for each range of values.

Would you like further details on any of these analyses, or have any specific questions?

Related questions:

  1. How do we calculate the median for this grouped data?
  2. What is the mean of the given data set?
  3. How can we calculate the variance and standard deviation for this data?
  4. What type of skewness does this frequency distribution suggest?
  5. How do we construct a histogram based on this data?

Tip:

When calculating the mean for grouped data, using the midpoint of each range provides a more accurate estimate than using the boundaries.

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Math Problem Analysis

Mathematical Concepts

Frequency Distribution
Mode
Median
Mean
Histogram

Formulas

Mode = Range with the highest frequency
Median = Midpoint of the cumulative frequency
Mean = (Σ(midpoint * frequency)) / Total Frequency

Theorems

Measures of Central Tendency
Grouped Data Analysis

Suitable Grade Level

Grades 6-9