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The histogram represents data collected on the frequency of how far the tide rose, in feet, up the beach from the buoy.

A histogram titled Tides For 15 Days with an x-axis labeled Measurement In Feet with intervals of 1 to 5, 6 to 10, 11 to 15, 16 to 20, and 21 to 25. The y-axis is labeled Frequency and starts at 0 with tick marks every one unit up to 7. There is a shaded bar above 1 to 5 that stops at 1, above 6 to 10 that stops at 3, above 11 to 15 that stops at 4, above 16 to 20 that stops at 4, and above 21 to 25 that stops at 3.

Which statement best describes the spread and distribution of the data?

The data is almost symmetric, with a maximum range of 24. This means that the tide frequently measured around 11 to 20 feet.
The data is skewed, with a maximum range of 24. This means that the tide was frequently very high in the 16 to 25 feet range.
The data is bimodal, with a maximum range of 24. This means that the tide was frequently between 6 to 10 or 21 to 25 feet.
The data is symmetric, with a maximum range of 20. This means that the tide frequently measured around 1 to 5 feet.

1 answer

To analyze the histogram's data, let's break down the key points regarding the frequency distribution of tide measurements:

  1. Data Ranges & Frequencies:

    • 1 to 5 feet: Frequency = 1
    • 6 to 10 feet: Frequency = 3
    • 11 to 15 feet: Frequency = 4
    • 16 to 20 feet: Frequency = 4
    • 21 to 25 feet: Frequency = 3

  2. Maximum Range: The maximum range indicated is from 1 to 25 feet, which suggests a range of 24 feet (25 - 1 = 24).

  3. Distribution Characteristics:

    • There are higher frequencies in the ranges of 11 to 15 feet and 16 to 20 feet, with both having a frequency of 4.
    • The frequencies for 6 to 10 feet and 21 to 25 feet are lower.
    • The lowest frequency is for 1 to 5 feet.

Given this data:

  • The data does not appear to be symmetric since the peak frequencies are within the middle ranges (11 to 20 feet) and decrease toward the lower end (1 to 5 feet) and also the higher end (21 to 25 feet).
  • The data does show a peak around 11 to 20 feet, indicating that these ranges are more frequent than the others, but it does not suggest a bimodal distribution.
  • The data does not have a clear maximum frequency out at the edges (lower or upper), suggesting it does not represent high tides at the 21 to 25 feet range frequently.

Based on these points, the best statement that describes the spread and distribution of the data is:

The data is skewed, with a maximum range of 24. This means that the tide was frequently very high in the 16 to 25 feet range.

This option appropriately captures the essence of the frequencies while noting the skewness towards the higher values, evidenced by the more frequent readings in the mid-to-upper ranges.