Math Problem Statement
Determine the 8th decile (D_8) of the data in the table provided, which shows the productive ages of residents in a certain area. Options: A. 32.5, B. 33.0, C. 33.5, D. 34.0, E. 34.5
Solution
The table in the image presents data on the ages of productive residents in a certain area. It also includes a question asking to determine the 8th decile (desil ke-8) of the data. The choices provided are as follows:
- A. 32.5
- B. 33.0
- C. 33.5
- D. 34.0
- E. 34.5
To find the 8th decile:
Deciles divide the data into 10 equal parts. The 8th decile, , represents the point below which 80% of the data lies.
Steps:
- Calculate the cumulative frequency for the data intervals.
- Find the position of the 8th decile using the formula: Here, the total frequency is , so:
- The 80th data point lies in the cumulative frequency range that includes 80 (by summing the frequencies for each age range).
- Use linear interpolation if needed to pinpoint the value of in the corresponding class.
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Math Problem Analysis
Mathematical Concepts
Statistics
Deciles
Frequency Distribution
Formulas
D_n = (n / 10) * Total Observations
Linear Interpolation for Decile Calculation
Theorems
Decile Calculation
Frequency Distribution Properties
Suitable Grade Level
Grades 10-12