Math Problem Statement

این دو تصویر را کاملا خلاصه و درست و مرتب و کوتاه جواب بده با توضیح

این دو تصویر را کاملا خلاصه و درست و مرتب و کوتاه جواب بده با توضیح

Solution

Image 1: Variance and Standard Deviation

Steps to Calculate Variance and Standard Deviation:

  1. Sample 1: x1=[18,19,20,21,22]x_1 = [18, 19, 20, 21, 22]

    • Mean (μ\mu): Calculate the average of values.
    • Variance (σ2\sigma^2): Compute (xiμ)2N\frac{\sum (x_i - \mu)^2}{N}, where NN is the sample size.
    • Standard Deviation (σ\sigma): Variance\sqrt{\text{Variance}}.
  2. Sample 2: x2=[90,4,3,2,1]x_2 = [90, 4, 3, 2, 1]

    • Repeat the same steps as Sample 1.

Image 2: Descriptive Statistics

For the dataset: [3,29,33,32,36,34,32,17,35,31,36,37,40,32,31,24][3, 29, 33, 32, 36, 34, 32, 17, 35, 31, 36, 37, 40, 32, 31, 24]:

  1. N: Count the number of data points.
  2. Mode: Most frequent value.
  3. Median: Middle value after sorting the data.
  4. Mean: Average of all values.
  5. Range: MaxMin\text{Max} - \text{Min}.
  6. Standard Deviation: Measure of data spread.

Would you like detailed calculations or additional clarifications? Let me know!

Related Questions:

  1. What is the difference between population and sample variance?
  2. How does the standard deviation help interpret data spread?
  3. What does a mode indicate about a dataset?
  4. Why is it essential to calculate a median along with the mean?
  5. How is the range useful for understanding variability?

Tip: Always double-check if the dataset includes outliers before calculating descriptive statistics, as they can skew the results.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Variance
Standard Deviation
Descriptive Statistics

Formulas

Mean: μ = (Σx) / N
Variance: σ² = Σ(xi - μ)² / N
Standard Deviation: σ = √Variance
Median: Middle value after sorting
Mode: Most frequent value
Range: Max - Min

Theorems

Statistical Properties of Variance and Standard Deviation
Measures of Central Tendency (Mean, Median, Mode)

Suitable Grade Level

Grades 10-12 or early undergraduate