Math Problem Statement

The data show the number of hours of television watched per day by a sample of 28 people. Use technology to answer parts​ (a) and​ (b) below.

6 8 7 2 0 5 0 8 3 3 2 6 6 4 8 4 8 1 9 3 0 6 6 4 7 3 6 6 Question content area bottom Part 1 a. Find the data​ set's first,​ second, and third quartiles. Upper Q 1 equals    enter your response here Upper Q 2 equals    enter your response here Upper Q 3 equals    6 8 7 2 0 5 0 8 3 3 2 6 6 4 8 4 8 1 9 3 0 6 6 4 7 3 6 6

Solution

The first, second, and third quartiles of the data set are as follows:

  • Q1=3.0Q_1 = 3.0 (First Quartile)
  • Q2=5.5Q_2 = 5.5 (Second Quartile or Median)
  • Q3=6.25Q_3 = 6.25 (Third Quartile)

Would you like further explanation on how these quartiles are calculated or need additional details?

Here are 5 related questions to explore:

  1. How are quartiles used to measure data spread?
  2. What is the interquartile range (IQR), and how can we calculate it for this dataset?
  3. How can outliers be identified using quartiles?
  4. What is the significance of the median in a dataset?
  5. How do quartiles compare with percentiles in data analysis?

Tip: Sorting the data is the first step in calculating quartiles and other percentile-based measures.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Statistics
Quartiles
Data Analysis

Formulas

Q1 = lower quartile (25th percentile)
Q2 = median (50th percentile)
Q3 = upper quartile (75th percentile)

Theorems

Quartile Theorem

Suitable Grade Level

Grades 9-12