Math Problem Statement

Calculate the mean and sample standard deviation of the data shown. Round your answers to two decimal places

x 25 29 24 16 12 28 20 Sample standard deviation =

Solution

import numpy as np

Data provided

data = np.array([25, 29, 24, 16, 12, 28, 20])

Calculating mean

mean = np.mean(data)

Calculating sample standard deviation

sample_std_dev = np.std(data, ddof=1)

mean, round(sample_std_dev, 2)(22.0, 6.3)(22.0, 6.3)successThe mean of the data is 22.0022.00, and the sample standard deviation is 6.306.30.

Would you like a detailed breakdown of the calculations or have any other questions? Here are some related questions for further exploration:

  1. How is the sample standard deviation formula different from the population standard deviation?
  2. Can you explain how to calculate variance from this data?
  3. What is the median of this data set?
  4. Are there any outliers in this data set? How would you identify them?
  5. How would adding another data point (e.g., 30) affect the mean and standard deviation?

Tip: Always ensure that you know whether to use sample or population formulas, as they differ slightly in terms of divisor adjustments!

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Math Problem Analysis

Mathematical Concepts

Statistics
Descriptive Statistics

Formulas

Mean formula: mean = (Σx) / n
Sample standard deviation formula: s = √[(Σ(x - mean)^2) / (n - 1)]

Theorems

None required

Suitable Grade Level

Grades 9-12