Lab 2 - Biometry work

MTH 280 - Biometry Lab 2 – Summary Statistics Population 100.0% maximum 72 99.5% 72 97.5% 72 90.0% 70 75.0% quartile 68.5 50.0% median 65 25.0% quartile 64 10.0% 62 2.5% 61 0.5% 61 0.0% minimum 61 Sample Mean 65.973684 Std Dev 3.1379119 Std Err Mean 0.7198864 Upper 95% Mean 67.486109 Lower 95% Mean 64.461259 N 19 N Missing 0 Mean 64.4 Std Dev 3.0495901 Std Err Mean 1.3638182 Upper 95% Mean 68.186566 Lower 95% Mean 60.613434 N 5 N Missing 0 100.0% maximum 68 99.5% 68 97.5% 68 90.0% 68 75.0% quartile 67.5 50.0% median 64 25.0% quartile 61.5 10.0% 61 2.5% 61 0.5% 61 0.0% minimum 61

1. For the height of the five randomly selected individuals, determine the sample mean and the sample median. Sample mean = 64.4 S ample median = 64 2. Compare and contrast the sample mean to the sample median . How close are the mean and median ? (Provide the actual difference between the two). Explain the reason(s) for the size of the difference if there is any. How useful is it to use a random sample of 5 individuals to represent the population? The sample median is the data located at the exact middle of the total observations (n). while the sample mean is an average of all the data. The mean and the median are close to a 0.4 difference. This difference is presented because the mean is an average of all data and if there are outliers or extreme values that can influence the mean. I don’t think a sample of 5 is a good representation of the population. 3. For the height of the population, determine the population mean and population median. Population mean = 65.9 Population median = 65 4. How well do the sample statistics estimate the population parameters ? In this case, there is not much difference. The values are closer to each other but for example, in a population, the max was 72 when in the sample size the max was 68. 5. What could we do to improve sample statistics’ estimation of population parameters ? Make sure that all the groups are represented and a min of 10 samples to represent a population.

8. Make side-by-side modified boxplots of the footprint traces based on sex Compare the modified boxplots of the footprint length data for the entire population ( use everyone NOT random sample ) to the two side-by-side modified boxplots of footprint length by sex. What does each boxplot tell you compared to the boxplot created regardless of sex? How would you decide which to use? The population boxplot has the quartiles in the meddle while the male boxplot is on the left and the female to the right. That means if I want have characteristic about population in general, using side by side I need to do an average between both means to have a better understand. Also, we can conclude that feet trace between sex are significant different. I prefer to use population boxplot. Descriptive statistics and measures of dispersion This exercise uses the Student Survey Results Fa2023 for height.

9. Calculate the sample standard deviation ( SD ) using JMP sample standard deviation (SD) is 3.7. 10. To calculate the population standard deviation: use JMP to get the “SD” of the population (full class data) following the directions for 9 but with the population data table. population standard deviation = 3.11 11. Using the 5 INDIVIDUAL RANDOM SAMPLES and the ENTIRE POPULATION (class data) , identify the SD (standard deviations). Why do you think these two are different (if they are)? If you only had the SD from the sample of 5 people, how would you know it is large or small? What does a large SD indicate regarding the data? What does it mean if the SD is small? sample standard deviation (SD) is 3.7. population standard deviation = 3.11

Using a quantitative variable that has a roughly symmetric and mound-shaped histogram from the Survey Data, see how well the Empirical Rule works. Approximate (make your best guess on visualizing the data) to get a sense of where you think ± 2 and 3 SD are from the mean (i.e. how far from the mean should you go to encompass 95% and 99.7% of the data? Use your ‘eyeball’ estimate to calculate the standard deviation ( s ). Creating and Formatting a Table Sex Height (in) Shoe size Age (month) Travel time to RCBC (min) # of Siblings Birth Order Screen time (min) Male 68 9.5 294 18 1 2 358 Female 62 7 249 10 0 1 496 Male 67 9.5 260 25 3 2 739 Female 64 8 243 15 5 2 213 Female 61 7 239 34 1 1 3765