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
- 70-74: 70, 70, 73, 71, 73, 73 → 6 days
- 75-79: 76, 76, 76, 79, 78, 76, 76, 75 → 8 days
- 80-84: 83, 84, 83, 84, 80, 80, 82 → 7 days
- 85-89: 86, 88, 88, 85, 88 → 5 days
- 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.
- 70-74: or 18.75%
- 75-79: or 25%
- 80-84: or 21.88%
- 85-89: or 15.63%
- 90-94: 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:
- What is the cumulative frequency for the ranges 70-84?
- How would you calculate the mode of the temperature data?
- What is the range of the given temperature data?
- Can you calculate the mean temperature for the month of June?
- 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
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