Question

MTH 243H- PCC (Trude) Name: 3. This data along the right is from the U.S. Department of Health and Human Services, National Center for Health Statistics, Third National Health and Nutrition Exam Survey. Recorded are the pulse rates from people who identify as female a. [4 pts] Fill in the table below outlining the summary statistics 60 60 60 64 64 64 64 Sample Size Mean Standard Deviation Minimum First Quartile Median Third Quartile Maximum 68 68 68 68 68 72 72 72 72 72 72 72 72 76 76 76 76 76 b. [4 pts] Construct a boxplot for the data. (Either by hand or using technology) 76 80 80 80 80 80 80 [4 pts] Summarize your findings by describing the shape, center, spread, and unusual features of the data c. 96 104 124

Answer 1

a) Sample Size: It is the no of Samples drawn, here it is 40

Mean is the average value of the sample calculated as

$M=\frac{X1+X2+X3.......+X40}{40}=\frac{60+60+60+.....+124}{40}=76.3$

Standard deviation is the spread of the data calculated as

$S=\sqrt{\frac{\sum (M-X_{i})^{2}}{n-1}}$

Sample standard deviation as 12.499

Minimum=60

First Quartile is the 25th percentile of data hence Q1=68

Median =(72+76)/2=74

Third Quartile=80

Maximum=124

b) The Box plot generated as

c) The Histogram of the data shown as

It suggests that the shape of data is not symmetric and not normally distributed and is right-skewed distribution.

Since the data is not symmetric so we should not use mean as the measure of central tendency, here it is convenient to use Median as central tendency parameter and Quartile data as its spread.