Math Problem Statement

Analyze the statistical problems from the uploaded image, which include calculating variance, mean, median, quartiles, range, and spread.

Solution

Let me analyze the image and solve the given questions.


Question 6: Variance (Ragam)

The data set is: 7, 8, 5, 7, 6, 8, 7, 6, 7, 8, 6, 7, 8, 6.

Steps:

  1. Find the Mean (xˉ\bar{x}):
    Mean xˉ=Sum of dataTotal data points\bar{x} = \frac{\text{Sum of data}}{\text{Total data points}}
    xˉ=7+8+5+7+6+8+7+6+7+8+6+7+8+614=6.93\bar{x} = \frac{7+8+5+7+6+8+7+6+7+8+6+7+8+6}{14} = 6.93 (

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Math Problem Analysis

Mathematical Concepts

Statistics
Variance
Mean
Median
Quartiles
Range
Spread

Formulas

Variance formula: σ² = Σ(x - μ)² / N
Mean formula: μ = Σx / N
Median formula: Position = (N + 1) / 2
Quartile formula: Qk = L + [(kN/4) - F] / f × c
Range formula: Max - Min
Spread formula: Interquartile Range (Q3 - Q1)

Theorems

Properties of central tendency
Properties of dispersion

Suitable Grade Level

Grades 10-12