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, D8D_8, represents the point below which 80% of the data lies.

Steps:

  1. Calculate the cumulative frequency for the data intervals.
  2. Find the position of the 8th decile using the formula: D8=810×total number of observationsD_8 = \frac{8}{10} \times \text{total number of observations} Here, the total frequency is 100100, so: D8=810×100=80D_8 = \frac{8}{10} \times 100 = 80
  3. The 80th data point lies in the cumulative frequency range that includes 80 (by summing the frequencies for each age range).
  4. Use linear interpolation if needed to pinpoint the value of D8D_8 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