Math Problem Statement

Berdasarkan set data pada Jadual 4, hitungkan (i) min (ii) Varians (iii) Sisihan piawai.

Solution

Let’s analyze and calculate based on the data provided in the image. The given table contains marks and the number of students, and we need to calculate:

  1. Mean (min)
  2. Variance
  3. Standard deviation (sisihan piawai)

Step 1: Prepare the Data

We calculate using the midpoint of each class interval (x) and the corresponding frequencies (f):

IntervalMidpoint (x)Frequency (f)f⋅xf \cdot xf⋅x2f \cdot x^2
10-1914.533⋅14.5=43.53 \cdot 14.5 = 43.53⋅14.523 \cdot 14.5^2
20-2924.511⋅24.5=24.51 \cdot 24.5 = 24.51⋅24.521 \cdot 24.5^2
30-3934.577⋅34.5=241.57 \cdot 34.5 = 241.57⋅34.527 \cdot 34.5^2
40-4944.51212⋅44.5=53412 \cdot 44.5 = 53412⋅44.5212 \cdot 44.5^2
50-5954.555⋅54.5=272.55 \cdot 54.5 = 272.55⋅54.525 \cdot 54.5^2
60-6964.522⋅64.5=1292 \cdot 64.5 = 1292⋅64.522 \cdot 64.5^2

Step 2: Calculate the Mean (Min)

The formula for the mean is:
xˉ=∑f⋅x∑f\bar{x} = \frac{\sum f \cdot x}{\sum f}

Step 3: Variance

Variance formula:
Variance=∑f⋅x2∑f−(xˉ)2\text{Variance} = \frac{\sum f \cdot x^2}{\sum f} - (\bar{x})^2

Step

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Math Problem Analysis

Mathematical Concepts

Statistics
Mean
Variance
Standard Deviation

Formulas

Mean: \( \bar{x} = \frac{\sum f \cdot x}{\sum f} \)
Variance: \( \sigma^2 = \frac{\sum f \cdot x^2}{\sum f} - (\bar{x})^2 \)
Standard Deviation: \( \sigma = \sqrt{\text{Variance}} \)

Theorems

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Suitable Grade Level

Grades 10-12

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