Math Problem Statement

The following is the average daily temperature for Frederick, Maryland for the month of June:

70 76 70 83 84 73 83 76 76 80 71 86 79 73 84 78 88 76 76 88 90 85 90 82 73 93 75 80 94 94 find the relative frequency for 70-74, 75-79, 80-84, 85-89, 90-94

Solution

To find the relative frequency for each temperature range (70-74, 75-79, 80-84, 85-89, and 90-94), we first need to count how many days fall within each of these ranges and then divide that count by the total number of data points.

Step 1: Organize the data

The temperatures for each day are as follows:

70, 76, 70, 83, 84, 73
83, 76, 76, 80, 71, 86
79, 73, 84, 78, 88, 76
76, 88, 90, 85, 90, 82
73, 93, 75, 80, 94, 94

Step 2: Count the number of days in each range

  1. 70-74: 70, 70, 73, 71, 73, 73 → 6 days
  2. 75-79: 76, 76, 76, 79, 78, 76, 76, 75 → 8 days
  3. 80-84: 83, 84, 83, 84, 80, 80, 82 → 7 days
  4. 85-89: 86, 88, 88, 85, 88 → 5 days
  5. 90-94: 90, 90, 93, 94, 94, 94 → 6 days

Step 3: Calculate total number of days

There are a total of 32 days.

Step 4: Calculate the relative frequency for each range

The relative frequency is the number of days in each range divided by the total number of days.

  1. 70-74: 632=0.1875\frac{6}{32} = 0.1875 or 18.75%
  2. 75-79: 832=0.25\frac{8}{32} = 0.25 or 25%
  3. 80-84: 732=0.21875\frac{7}{32} = 0.21875 or 21.88%
  4. 85-89: 532=0.15625\frac{5}{32} = 0.15625 or 15.63%
  5. 90-94: 632=0.1875\frac{6}{32} = 0.1875 or 18.75%

Summary of relative frequencies:

  • 70-74: 18.75%
  • 75-79: 25%
  • 80-84: 21.88%
  • 85-89: 15.63%
  • 90-94: 18.75%

Would you like more details or have any questions?


Here are 5 related questions for further practice:

  1. What is the cumulative frequency for the ranges 70-84?
  2. How would you calculate the mode of the temperature data?
  3. What is the range of the given temperature data?
  4. Can you calculate the mean temperature for the month of June?
  5. What would the relative frequency be if there were 40 days of temperature data?

Tip: To double-check your relative frequency calculation, always ensure that the sum of the relative frequencies equals 100%.

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Math Problem Analysis

Mathematical Concepts

Statistics
Relative Frequency
Frequency Distribution

Formulas

Relative frequency = (Number of occurrences in a range) / (Total number of data points)

Theorems

Law of Large Numbers

Suitable Grade Level

Grades 8-10