Math Problem Statement

Given below are data that has approximately normal distribution.

data data data data 59.36 58.86 61.31 54.32 58.37 48.06 33.47 59.71 41.47 34.47 53.26 61.1 44.07 43.39 48.02 60.55 57.11 53.84 58.65 34.99 59.52 66.87 32.46 32.86 53.86 66.14 50.77 43.12 48.24 42.85 48.5 39.34 42.74 57.97 68.27 60 55 52.37 48.98 65

In building a grouped frequency distribution table for this data set, how many values are there in the class 60-64.99? Include the lower class limit, but not the upper class limit.

Solution

To find out how many values fall into the class interval 6064.9960 - 64.99 (including 60 but excluding 65), we'll follow these steps:

Steps:

  1. Identify the data points in the interval 60x<6560 \leq x < 65.
  2. Count the data points that fall within this range.

Data points provided:

59.36, 58.86, 61.31, 54.32, 58.37, 48.06, 33.47, 59.71, 41.47, 34.47, 53.26, 61.10, \\ 44.07, 43.39, 48.02, 60.55, 57.11, 53.84, 58.65, 34.99, 59.52, 66.87, 32.46, 32.86, \\ 53.86, 66.14, 50.77, 43.12, 48.24, 42.85, 48.50, 39.34, 42.74, 57.97, 68.27, 60.00, \\ 55.00, 52.37, 48.98, 65.00 \end{aligned}$$ #### Data in the interval $$60 \leq x < 65$$: - 61.31 - 61.10 - 60.55 - 60.00 There are **4 values** in the class interval $$60 - 64.99$$. ### Conclusion: There are **4 values** in the class $$60 - 64.99$$, including the lower class limit but excluding the upper class limit. --- Would you like more details on how to organize the frequency distribution? Here are some related questions: 1. How to construct a grouped frequency distribution table? 2. How to calculate the mean and standard deviation for this data? 3. What is a normal distribution, and how can this data be tested for normality? 4. How can we visualize this data set with a histogram or frequency polygon? 5. How can we calculate the cumulative frequency for this data? **Tip**: Grouped frequency tables are helpful when dealing with large data sets, making it easier to spot trends and calculate descriptive statistics.

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Math Problem Analysis

Mathematical Concepts

Statistics
Frequency Distribution
Class Intervals

Formulas

Frequency distribution formula: Count values in the interval x ≤ value < y

Theorems

Empirical Rule for Normal Distribution

Suitable Grade Level

Grades 10-12