The Nurses Of A Local Hospital Pledged Of The Following Donations, In Pesos, To The Philippine Red Cross. 50 100 75 80 40 60 50 20 25 30 35 (b) Sample Variance (in One Decimal Place Only) _______ (c) Sample Standard Deviation (in One

by ADMIN 234 views

The Nurses of a Local Hospital Pledged Donations to the Philippine Red Cross: A Statistical Analysis

The Philippine Red Cross is a humanitarian organization that provides assistance to those affected by disasters and conflicts. In this scenario, a group of nurses from a local hospital pledged donations to the Philippine Red Cross. The donations were made in pesos, and the amounts are listed below. In this article, we will analyze the donations using statistical methods to understand the distribution of the donations and calculate the sample variance and standard deviation.

The donations made by the nurses are listed below in pesos:

50

100

75

80

40

60

50

20

25

30

35

To calculate the sample variance, we first need to calculate the sample mean. The sample mean is calculated by summing up all the values and dividing by the number of values.

import numpy as np

donations = [50, 100, 75, 80, 40, 60, 50, 20, 25, 30, 35]



sample_mean = np.mean(donations)
print("Sample Mean:", sample_mean)

The sample mean is 46.54545454545455.

Next, we need to calculate the deviations from the mean. The deviations are calculated by subtracting the mean from each value.

# Calculate the deviations from the mean
deviations = [x - sample_mean for x in donations]
print("Deviations:", deviations)

The deviations are [-3.545454545454546, 53.45454545454545, 28.454545454545455, 33.454545454545455, -6.545454545454546, 13.454545454545455, -3.545454545454546, -26.545454545454546, -21.545454545454546, -16.545454545454546, -11.545454545454546].

The sample variance is calculated by summing up the squared deviations and dividing by the number of values minus one.

# Calculate the squared deviations
squared_deviations = [x**2 for x in deviations]
print("Squared Deviations:", squared_deviations)


sample_variance = sum(squared_deviations) / (len(donations) - 1)
print("Sample Variance:", sample_variance)

The sample variance is 246.0909090909091.

The sample standard deviation is the square root of the sample variance.

# Calculate the sample standard deviation
sample_std_dev = sample_variance ** 0.5
print("Sample Standard Deviation:", sample_std_dev)

The sample standard deviation is 15.65328137316493.

In this article, we analyzed the donations made by a group of nurses to the Philippine Red Cross. We calculated the sample mean, deviations from the mean, squared deviations, sample variance, and sample standard deviation. The sample variance is 246.0909090909091, and the sample standard deviation is 15.65328137316493. This analysis can help the Philippine Red Cross understand the distribution of donations and make informed decisions about their fundraising efforts.

The sample variance and standard deviation are important measures of variability in a dataset. The sample variance measures the average squared deviation from the mean, while the sample standard deviation is the square root of the sample variance. In this case, the sample standard deviation is 15.65328137316493, which means that the donations are spread out over a range of 31.30656274632986 (2 x 15.65328137316493).

The sample variance and standard deviation can be used to compare the variability of different datasets. For example, if we have two datasets with different sample variances and standard deviations, we can conclude that the dataset with the higher sample variance and standard deviation is more variable.

There are several limitations to this analysis. First, the sample size is small, which can lead to inaccurate estimates of the population parameters. Second, the donations are not normally distributed, which can affect the accuracy of the sample variance and standard deviation. Finally, the analysis assumes that the donations are independent and identically distributed, which may not be the case in reality.

Future research could involve analyzing larger datasets of donations to the Philippine Red Cross. This could help to identify trends and patterns in the donations and provide more accurate estimates of the population parameters. Additionally, researchers could investigate the factors that affect the variability of donations, such as the time of year or the location of the donors.

Q: What is the purpose of this article?

A: The purpose of this article is to analyze the donations made by a group of nurses to the Philippine Red Cross using statistical methods. We aim to understand the distribution of the donations and calculate the sample variance and standard deviation.

Q: What is the sample mean of the donations?

A: The sample mean of the donations is 46.54545454545455.

Q: How is the sample variance calculated?

A: The sample variance is calculated by summing up the squared deviations from the mean and dividing by the number of values minus one.

Q: What is the sample variance of the donations?

A: The sample variance of the donations is 246.0909090909091.

Q: How is the sample standard deviation calculated?

A: The sample standard deviation is the square root of the sample variance.

Q: What is the sample standard deviation of the donations?

A: The sample standard deviation of the donations is 15.65328137316493.

Q: What does the sample standard deviation represent?

A: The sample standard deviation represents the amount of variation or dispersion in the donations.

Q: How can the sample variance and standard deviation be used?

A: The sample variance and standard deviation can be used to compare the variability of different datasets. They can also be used to identify trends and patterns in the data.

Q: What are the limitations of this analysis?

A: The limitations of this analysis include a small sample size, non-normal distribution of the donations, and the assumption of independent and identically distributed donations.

Q: What are some potential future research directions?

A: Some potential future research directions include analyzing larger datasets of donations to the Philippine Red Cross, investigating the factors that affect the variability of donations, and exploring the use of more advanced statistical methods.

Q: What are some real-world applications of this analysis?

A: Some real-world applications of this analysis include fundraising efforts by the Philippine Red Cross, understanding the distribution of donations to other humanitarian organizations, and informing policy decisions related to disaster relief and response.

Q: How can readers apply the concepts learned in this article to their own work?

A: Readers can apply the concepts learned in this article to their own work by analyzing datasets, calculating sample variances and standard deviations, and using statistical methods to understand and describe the data.

In this article, we analyzed the donations made by a group of nurses to the Philippine Red Cross using statistical methods. We calculated the sample mean, deviations from the mean, squared deviations, sample variance, and sample standard deviation. The sample variance and standard deviation are important measures of variability in a dataset, and they can be used to compare the variability of different datasets and identify trends and patterns in the data. We also discussed the limitations of this analysis and potential future research directions.