Math Problem Statement

23, 21, 18, 23, 28, 15, 8, 16 what is the mean, median, Q1 and Q3 of this data set

Solution

import numpy as np import pandas as pd

Data set

data = [23, 21, 18, 23, 28, 15, 8, 16]

Sorting the data for easier calculation

sorted_data = sorted(data)

Calculating mean, median, Q1, and Q3

mean = np.mean(data) median = np.median(data) q1 = np.percentile(data, 25) q3 = np.percentile(data, 75)

mean, median, q1, q3(19.0, 19.5, 15.75, 23.0)(19.0, 19.5, 15.75, 23.0)successFor the given data set [23, 21, 18, 23, 28, 15, 8, 16], the statistical measures are as follows:

  • Mean (Average): 19.0
  • Median: 19.5
  • First Quartile (Q1): 15.75
  • Third Quartile (Q3): 23.0

Do you want a detailed explanation or visualization of these calculations?

Expanding Questions:

  1. How can the data be interpreted in terms of spread and outliers?
  2. Would you like to calculate the range, variance, or standard deviation?
  3. How would these measures change if another value were added to the data set?
  4. What is the significance of Q1 and Q3 in understanding the data distribution?
  5. Would you like to see this data represented graphically (e.g., box plot)?

Tip:

Using quartiles helps identify skewness and potential outliers in a data set effectively!

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Math Problem Analysis

Mathematical Concepts

Descriptive Statistics
Mean
Median
Quartiles

Formulas

Mean = (Sum of all data points) / (Number of data points)
Median = Middle value in a sorted data set (or average of two middle values for even-sized sets)
Q1 = 25th percentile of the data
Q3 = 75th percentile of the data

Theorems

Percentile calculation for quartiles

Suitable Grade Level

Grades 6-9