Math Problem Statement

Bei einem 100-m-Lauf werden in der Klasse F2a folgende Zeiten (in Sekunden) gestoppt: 11.8, 12.0, 12.2, 12.5, 12.6, 12.7, 12.8, 12.9, 13.1, 13.1, 13.3, 13.4, 13.5, 13.6, 13.6, 13.8, 13.9, 14.2, 14.3, 14.5, 14.5, 14.7, 15.0, 15.1 und 15.1. a) Nehmen Sie eine Klasseneinteilung vor. b) Berechnen Sie den Mittelwert nach Klasseneinteilung. c) Berechnen Sie den Mittelwert ohne Klasseneinteilung. Die Altersstruktur der Bevölkerung in der Schweiz am Jahresende 2005: Alter (Jahre) 0 ≤ x ≤ 19 20 ≤ x ≤ 39 40 ≤ x ≤ 64 65 ≤ x ≤ 79 80 und älter Gesamt.

Solution

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Problem 165:

You have a set of times from a 100-meter run. The goal is to: a) Create class intervals (classeninteilung). b) Calculate the mean for the class intervals. c) Calculate the mean without class intervals.

Steps:

  1. Class intervals will be chosen by determining suitable ranges based on the times.
  2. Mean with class intervals involves multiplying the class midpoint by the frequency of each class and dividing the sum by the total number of times.
  3. Mean without class intervals involves directly averaging the recorded times.

Problem 166:

This question provides data on the age structure of the population in Switzerland in 2005 and asks: a) Calculate the relative frequency. b) Create a pie chart (Kreisdiagramm). c) Estimate the average age based on the population data, assuming a maximum age of 100 years.

I'll break down each question further, and we can calculate the necessary values step-by-step.

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Math Problem Analysis

Mathematical Concepts

Statistical Analysis
Class Intervals
Mean Calculation
Relative Frequency

Formulas

Mean with Class Intervals = Σ (midpoint * frequency) / total
Mean without Class Intervals = Σ (values) / number of values

Theorems

Central Limit Theorem
Mean Calculation Theorem

Suitable Grade Level

Grades 10-12