MATH 225 Week 5 Assignment: Lab

Grace J.
August 7, 2025August 7, 2025
CU BSN, MATH-225

Student Name

Chamberlain University

MATH-225 Statistical Reasoning for the Health Sciences

Prof. Name

Date

Week 5 Lab Assignment

Height Data Collection and Sampling Method

For this study, data was gathered regarding the height of ten female acquaintances. The information was collected informally through verbal responses rather than physical measurements, which introduces potential inaccuracies. The method employed to gather this data is classified as a convenience sampling technique, where participants were readily accessible and willingly provided their self-reported heights via a group text message. This approach, while practical, increases the likelihood of bias and reduces the overall validity of the results. The potential for error is further heightened due to subjective responses like, “I think I’m around 5’6” or “last time I checked I was 5’4”. Such approximations diminish the precision of the data set.

Raw Height Data

The collected height data (in inches) is listed below:

Participant	Height (in inches)
1	64
2	64
3	65
4	65
5	66
6	66
7	66
8	67
9	67
10	69

Descriptive Statistics

Using Excel to analyze the sample, the following descriptive statistics were calculated:

Statistical Measure	Value
Mean	65.9000
Median	66.0000
Mode	66.0000
Sample Variance	2.3222
Sample Standard Deviation	1.5239
Population Variance	2.0900
Population Std. Deviation	1.4457
Range	5.0000
First Quartile (Q1)	64.7500
Third Quartile (Q3)	67.0000
Interquartile Range (IQR)	2.2500
Maximum	69.0000

How does your height compare to the mean (average) height of the group that you surveyed?

My height is 5 feet 3 inches, which is 63 inches. This is shorter than the group’s average height of 65.9 inches.

How did you choose the participants for your study (sampling method)?

The data was gathered using convenience sampling. Due to restrictions during the COVID-19 pandemic, participants were chosen from a group of my friends and contacted via text message. While this method is convenient, it introduces sampling bias due to lack of randomization.

What part of the country did your study take place in?

The study was conducted in California, specifically in the Sacramento area.

What are the age ranges of your participants?

The participants in this sample were between the ages of 29 and 35 years.

How many of each gender did you have in your study?

The entire sample consisted of 10 female participants only.

What are other interesting factors about your group?

All participants are personal acquaintances, and most reside in California. The group is predominantly Caucasian, with 2 participants identifying as Hispanic. Interestingly, the two Hispanic women were the shortest among the group, though I was shorter than them all. Also, due to self-reported heights, some responses may be inaccurate, adding further bias to the sample.

Z-Score Calculation for a Given Height

To calculate the Z-score for a person who is 64 inches tall:

Formula:
Z = (x – mean) / standard deviation
Z = (64 – 65.9) / 1.5239 ≈ -1.2466

Empirical Rule Analysis

Using the Empirical Rule (68-95-99.7), we can determine the expected height ranges within each standard deviation from the mean.

Coverage	Lower Bound	Upper Bound
68% (±1σ)	64.3761	67.4240
95% (±2σ)	62.8522	68.9480
99.7% (±3σ)	61.3283	70.4720

Interpretation:

68% of the heights fall between 64.4 and 67.4 inches
95% fall between 62.9 and 68.9 inches
99.7% fall between 61.3 and 70.5 inches

Given my height of 63 inches, this falls below the 68% and 95% range, indicating I am shorter than approximately 97.15% of the population in this sample.