Skip to ContentGo to accessibility pageKeyboard shortcuts menu
OpenStax Logo
Introductory Statistics

6.4 Normal Distribution (Pinkie Length)

Introductory Statistics6.4 Normal Distribution (Pinkie Length)

Stats Lab

Normal Distribution (Pinkie Length)

Class Time:

Names:

Student Learning Outcomes
  • The student will compare empirical data and a theoretical distribution to determine if data from the experiment follow a continuous distribution.

Collect the Data Measure the length of your pinky finger (in centimeters).

  1. Randomly survey 30 adults for their pinky finger lengths. Round the lengths to the nearest 0.5 cm.
    Table 6.2
  2. Construct a histogram. Make five to six intervals. Sketch the graph using a ruler and pencil. Scale the axes.
    Blank graph with frequency on the vertical axis and length of finger on the horizontal axis.
    Figure 6.11
  3. Calculate the following.
    1. x ¯ x ¯ = _______
    2. s = _______
  4. Draw a smooth curve through the top of the bars of the histogram. Write one to two complete sentences to describe the general shape of the curve. (Keep it simple. Does the graph go straight across, does it have a v-shape, does it have a hump in the middle or at either end, and so on?)

Analyze the Distribution Using your sample mean, sample standard deviation, and histogram, what was the approximate theoretical distribution of the data you collected?

  • X ~ _____(_____,_____)
  • How does the histogram help you arrive at the approximate distribution?

Describe the Data Using the data you collected complete the following statements. (Hint: order the data)

Remember

(IQR = Q3 – Q1)

  • IQR = _______
  • The 15th percentile is _______.
  • The 85th percentile is _______.
  • Median is _______.
  • What is the theoretical probability that a randomly chosen pinky length is more than 6.5 cm?
  • Explain the meaning of the 85th percentile of this data.

Theoretical Distribution Using the theoretical distribution, complete the following statements. Use a normal approximation based on the sample mean and standard deviation.

  • IQR = _______
  • The 15th percentile is _______.
  • The 85th percentile is _______.
  • Median is _______.
  • What is the theoretical probability that a randomly chosen pinky length is more than 6.5 cm?
  • Explain the meaning of the 85th percentile of this data.

Discussion QuestionsDo the data you collected give a close approximation to the theoretical distribution? In complete sentences and comparing the results in the sections titled Describe the Data and Theoretical Distribution, explain why or why not.

PreviousNext
Order a print copy
Citation/Attribution

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute OpenStax.

Attribution information
  • If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:
    Access for free at https://openstax.org/books/introductory-statistics/pages/1-introduction
  • If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:
    Access for free at https://openstax.org/books/introductory-statistics/pages/1-introduction
Citation information

© Jun 23, 2022 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.