Math Problem Statement

Solve using Constructing Frequency Distribution

  1. Determine as to estimate number of classes k, k = 1 + 3 log n, where n is the number of populations
  2. Determine the range, r = highest values- lowest value
  3. Obtain the class size, c = r/k
  4. Set the lowest value as the first lower limit and get the upper limit which is equal to first lower limi+ class size -1.
  5. Do the same process again until you reach the last class limit that includes the highest value from the data.
The following data below represents the weekly duty hours of nursing students: 29, 28, 33, 25, 30, 28, 40, 36, 30, 28, 42, 33, 37, 30, 40, 32, 31, 28, 41, 35, 34, 35, 36, 31, 29, 39, 41, 31, 31, 34, 40, 42, 38, 33, 36, 37, 32, 40, 30, 37, 35, 33, 41, 29, 29, 30, 35, 34, 39, 31, 28, 31, 31, 30, 32, 30, 29, 30, 36, 31, 41, 38, 38, 33. Construct the frequency distribution and then find the mean, median, and mode.

Solution

Here's the frequency distribution and summary statistics based on the data provided:

Frequency Distribution:

  • [25.0, 28.0): 3 occurrences
  • [28.0, 31.0): 12 occurrences
  • [31.0, 34.0): 22 occurrences
  • [34.0, 37.0): 9 occurrences
  • [37.0, 40.0): 10 occurrences
  • [40.0, 43.0): 5 occurrences

Summary Statistics:

  • Mean (average): 33.26
  • Median (middle value): 32.0
  • Mode (most frequent value): 31

Would you like further details or have any questions?

Related Questions:

  1. How can the mean be interpreted in this context?
  2. How does the range of the data affect the class size?
  3. Why is the mode important in this dataset?
  4. How does changing the number of classes impact the frequency distribution?
  5. How would you handle any outliers in this data set?

Tip:

When constructing a frequency distribution, always check if the class intervals overlap, as it can lead to confusion in data interpretation.

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Math Problem Analysis

Mathematical Concepts

Statistics
Frequency Distribution
Measures of Central Tendency

Formulas

k = 1 + 3 log n (Sturges' formula for number of classes)
r = highest value - lowest value (range)
c = r/k (class width)
Mean = (Σx) / n
Median = middle value in sorted data
Mode = most frequent value in data

Theorems

Sturges' Rule for Determining the Number of Classes

Suitable Grade Level

Grades 9-12

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