Math Problem Statement

Consider the frequency distribution with 5 classes of the given data set that represents the time in minutes spent reading a music blog in a day. Data Set: 

7,39,13,25,8,22,0,2,18,2,30,7,35,12,15,8,6,5,29,0,11,39,16,15

Give the the class width, the lower class limit of the first class, and the upper class limit of the first class. Separate your answers with commas.  

Solution

To solve this, we first follow these steps:

  1. Class Width:
    The class width is determined by finding the difference between the maximum and minimum values of the dataset and dividing by the number of classes. Then, round up to the nearest whole number.

    Class width=Max valueMin valueNumber of classes\text{Class width} = \frac{\text{Max value} - \text{Min value}}{\text{Number of classes}}

    • Max value = 39
    • Min value = 0
    • Number of classes = 5

    Class width=3905=395=7.88\text{Class width} = \frac{39 - 0}{5} = \frac{39}{5} = 7.8 \approx 8

  2. Lower Class Limit of the First Class:
    The lower class limit of the first class is the minimum value in the dataset, which is 0.

  3. Upper Class Limit of the First Class:
    The upper class limit of the first class can be found by adding the class width to the lower class limit of the first class and then subtracting 1 to avoid overlap between classes.

    Upper class limit of the first class=0+81=7\text{Upper class limit of the first class} = 0 + 8 - 1 = 7

Final Answer:

Class width = 8, Lower class limit = 0, Upper class limit = 7

Would you like further details on the steps or have any questions?

Here are 5 related questions you might find helpful:

  1. How would the class limits change if we used 6 classes instead of 5?
  2. What are the limits of the second class in this distribution?
  3. How do you find the class midpoint, and what is it for the first class?
  4. How would the frequency distribution look for this dataset?
  5. Why do we round up the class width?

Tip: Always remember to subtract 1 from the upper class limit to ensure no overlap between consecutive classes.

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Math Problem Analysis

Mathematical Concepts

Statistics
Frequency Distribution
Class Width
Class Limits

Formulas

Class width = (Max value - Min value) / Number of classes
Upper class limit = Lower class limit + Class width - 1

Theorems

-

Suitable Grade Level

Grades 9-12