Question

Blood pH A medical laboratory tested 21 samples of human blood for acidity on the pH scale, with the following results. $\begin{array}{llllll}{7.1} & {7.5} & {7.3} & {7.4} & {7.6} & {7.2} & {7.3} \\ {7.4} & {7.5} & {7.3} & {7.2} & {7.4} & {7.3} & {7.5} \\ {7.5} & {7.4} & {7.4} & {7.1} & {7.3} & {7.4} & {7.4}\end{array}$ a. Find the mean and standard deviation. b. What percentage of the data is within 2 standard deviations of the mean?

Name: Problem 31, Chapter 9: Finite Mathematics and Calculus with Applications
Uploaded: 2023-07-12T21:18:40-08:00
Duration: 1 min 5 s
Channel: Matthew Winsor
Description: Blood pH A medical laboratory tested 21 samples of human blood for acidity on the pH scale, with the following results. 7.1 7.5 7.3 7.4 7.6 7.2 7.3 7.4 7.5 7.3 7.2 7.4 7.3 7.5 7.5 7.4 7.4 7.1 7.3 7.4 7.4 a. Find the mean and standard deviation. b. What percentage of the data is within 2 standard deviations of the mean?

   Blood pH A medical laboratory tested 21 samples of human blood for acidity on the pH scale, with the following results.
$\begin{array}{llllll}{7.1} & {7.5} & {7.3} & {7.4} & {7.6} & {7.2} & {7.3} \\ {7.4} & {7.5} & {7.3} & {7.2} & {7.4} & {7.3} & {7.5} \\ {7.5} & {7.4} & {7.4} & {7.1} & {7.3} & {7.4} & {7.4}\end{array}$
a. Find the mean and standard deviation.
b. What percentage of the data is within 2 standard deviations of the mean?

Finite Mathematics and Calculus with Applications

Margaret L. Lial,… 9th Edition

Chapter 9, Problem 31

Instant Answer

Solved by Expert Matthew Winsor

07/12/2023

Step 1

The sum of the data, denoted as $\sum x$, is 154.5 and the sum of the squares of the data, denoted as $\sum x^2$, is 1137.3. Show more…

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Blood pH A medical laboratory tested 21 samples of human blood for acidity on the pH scale, with the following results. $\begin{array}{llllll}{7.1} & {7.5} & {7.3} & {7.4} & {7.6} & {7.2} & {7.3} \\ {7.4} & {7.5} & {7.3} & {7.2} & {7.4} & {7.3} & {7.5} \\ {7.5} & {7.4} & {7.4} & {7.1} & {7.3} & {7.4} & {7.4}\end{array}$ a. Find the mean and standard deviation. b. What percentage of the data is within 2 standard deviations of the mean?

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Key Concepts

Mean

The mean is the arithmetic average of a set of values and serves as a measure of central tendency. It is calculated by summing all the data points and dividing by the number of data points, providing a single value that represents the center of the data distribution.

Standard Deviation

Standard deviation is a statistic that measures the dispersion or spread of data values around the mean. It represents the typical distance between each data point and the mean, giving insight into how much variability exists within the dataset.

Data Dispersion and Standard Deviation Intervals

Analyzing the percentage of data within a certain number of standard deviations from the mean is a fundamental aspect of descriptive statistics. This concept, often illustrated by the empirical rule in normally distributed data, helps in understanding the concentration of data values around the mean, though general methods, like Chebyshev’s Theorem, apply to any distribution.

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