# NURS 8201 Frequency and Descriptive Statistics

## NURS 8201 Frequency and Descriptive Statistics

NURS 8201 Frequency and Descriptive Statistics

There are a few key reasons why frequencies and descriptive statistics are important in data analysis. First, frequencies can help a researcher to get a better understanding of the dataset. By looking at the distribution of data, data analysts can identify any outliers or unusual values, and this can help in the determination of the best methods to use. Second, descriptive statistics can be used to summarize data; this includes things like the mean, median, and mode, which can give an idea of the typical value in the dataset or how skewed the data is (Cooksey, 2020). Lastly, frequencies and descriptive statistics can be used to identify patterns in the data and to decide whether to apply parametric or non-parametric tests in the process of data analysis. The purpose of this assignment is to reflect and interpret the frequency distributions and descriptive statistics presented in the SPSS output.

### Interpretation of the Frequency Data

The frequency data from SPSS output can be interpreted in a few different ways. One way to interpret the data is to look at the percentage of cases that fall into each category. This can be done by dividing the number of cases in a category by the total number of cases and multiplying by 100. Another way to interpret the data is to look at the absolute frequencies. This can be done by counting how many cases fall into each category (Cooksey, 2020). From the SPSS output, the frequency data for the respondent’s age is represented by the histogram, as shown in graph 1 below.

### Graph 1: Frequency Distribution for Respondent’s Age at Time of Interview

The frequency distribution shows that the respondent’s age variable has a normal distribution with a mean of 36.64 and a standard deviation of 6.199. From the graph, out of 1000 respondents interviewed, the majority, 80%, were at the age of 40 years. The majority of the respondents were between the age of 35 and 42 years, constituting over 65% of the total respondents. Finally, less than 5% of the respondent were below the age of 20 years and above 50 years.

### Graph 2: Frequency Distribution Highest School Grade Completed

Graph 2 indicates the frequency of highest school grades completed. The distribution of data is leptokurtic, with a mean of 11.28 and a standard deviation of 1.561. The total number of respondents who recorded their grades was 989. The highest grade completed was 16, while the least grade was 1. The majority of respondents, 300, had 11 as the highest school grade completed, while 280 respondents had 12 as the highest school grade completed. Overall, the majority of the respondents had between 9 and 14 as the highest grades completed.

### Graph 3: Frequency for Family Income from Prior Month

Graph 3 shows the frequency distribution for the family income from the prior month. The graph is positively skewed, with a mean of \$1,172.59 and a standard deviation of \$788.153. The total number of respondents who recorded their family income was 895. Majority of the people earned between \$0 and \$2,000 from the prior month. The highest income earner from the prior month got \$ 6,593, while the least earner got \$0. The majority of the respondents got \$1,000 as the family income from the prior month.

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### Interpretation of the Descriptive Statistics

The descriptive statistics provide a summary of the key features of the data. Descriptive statistics often involve the analysis of mean, median, mode, standard deviation, sample size, range, Skewness, etc. (Mishra et al., 2019). The mean of a set of data is the sum of all the data points divided by the number of data points. The mode is the value that appears most often in a set of data. The standard deviation measures how dispersed the data are around the mean. The maximum is the largest value in a set of data, and the minimum is the smallest value.

#### Table 1: Respondent’s Age

Table 1 shows the descriptive statistics for the respondent’ age. From the table, the total number of respondents interviewed was 1000; the minimum age was 19, while the maximum age was 50. The average age of the respondents was 36.64, with a standard deviation of 6.19874. The data showed a slight negative Skewness with a coefficient of -0.374. From the descriptive statistics, parametric tests can be applied in the analysis of data.

#### Table 2: Highest School Grade Completed

From table 2, a total of 989 respondents were interviewed. The mean highest grade completed was 11.28, with a standard deviation of 1.561. The highest school grade completed was 16, while the minimum school grade completed was 1. The distribution of the highest grade completed was leptokurtic. In other words, the Skewness had a coefficient of -0.727 and a standard error of 0.078.

#### Table 3: Descriptive Statistics for Race and Ethnicity

Table 3 indicates the descriptive statistics for the Race and Ethnicity variable. The data shows a total sample size of 1000, with the highest participants being Black, not Hispanic at 80.3%, followed by Hispanic at 12.8%. Other races constituted 1.4% of the total respondents. Two respondents did not participate in answering the question about race.

#### Table 4: Descriptive Statistics on Currently Employed

From table 4, out of 1000 respondents sampled, two responses were missing. 54.7% of respondents were unemployed, while 45.3% were employed. The sample size used was 1000.

#### Table 4: Descriptive Statistics for Family Income

The sample size used in the computation of descriptive statistics about family income was 895. The minimum family income from the prior month was \$ 0, while the maximum income was \$ 6,593. The average family income from the prior month was \$ 1, 172.59 with a standard deviation of \$788.153. The data was positively skewed with a coefficient of 2.030 and a standard error of 0.082.

### Conclusion

The descriptive statistics show that parametric tests can be applied to prove that hypothesis and answer the research questions. From the tables and graphs, the sample size used was consistent for all the variables, hence the validity of the findings. There are a few key reasons why frequencies and descriptive statistics are important in data analysis. First, frequencies can help a researcher to get a better understanding of the dataset.

### References

Cooksey, R. W. (2020). Descriptive statistics for summarising data. In Illustrating statistical procedures: Finding meaning in quantitative data (pp. 61-139). Springer, Singapore. https://link.springer.com/chapter/10.1007/978-981-15-2537-7_5

Mishra, P., Pandey, C. M., Singh, U., Gupta, A., Sahu, C., & Keshri, A. (2019). Descriptive statistics and normality tests for statistical data. Annals of cardiac anaesthesia22(1), 67. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6350423/

Descriptive statistics help researchers to understand the nature of the data and to summarize it in a way that is easy to understand. In particular, descriptive statistics can be used to calculate things like the mean, median, and mode of a set of data, as well as to calculate various measures of variability (such as standard deviation and variance) (Haden, 2019). This information can then be used to help researchers develop exploratory models and conceptual models for their data. This assignment involves conducting descriptive statistical analyses of various social demographic variables and how they relate to one another. The data includes respondents’ age, Highest School Grade Completed, Race and Ethnicity, Currently Employed, and family income information. By gleaning insights found in correlations between the different variables, it will be possible to gain an understanding of certain dynamics that could potentially influence related factors. Moreover, these types of analyses allow researchers to compare statistics from different time frames and locations in order to better understand the changing nature of the research.

### Part I

#### Table 1: Respondent’s Age

From table 1, the maximum age of the respondents was 49.43 while the minimum age was 19.38 at the time of interview. The mean age of the respondents was 36.64 with a standard deviation of 6.20. A total of 1000 respondents were involved in the study.

#### Table 2: Highest School Grade Completed

From table 2, 11 respondents did not state the highest school grade completed. However, from those who answered this question, the highest grade completed was 16 while lowest grade was 1.

#### Table 3: Race and Ethnicity

Table 3 shows frequency distribution for respondent’s race and ethnicity. The outcome shows that majority of the respondents (80.3%) Blacks, not Hispanic. 12.8% of the respondents were Hispanic while 5.3% were Whites, not Hispanic. Only 1.4% of respondents were from other races not mentioned. Finally, 0.1% refused to state their race; 99.8% of study participants responded to the question on race and ethnicity.

#### Table 4: Currently Employed

Out of 1000 respondents sampled for the study, 54.6% were unemployed while 45.2% had employment; 0.2% did not reveal their employment status. 99.8% of the study participates respondent to a question on employment status.

### Part II

#### Graph 1: Frequency Distribution of Respondent’s Age at Time of Interview

From graph 1, data on respondent’ age exhibited a normal distribution with mean 36.64 and a standard deviation of 6.199. Majority of the respondents were between the age of 30 and 45 years. Less than 40% of respondents were below 30 years of age.

#### Graph II: Frequency Distribution for Highest School Grade Completed

From Graph II, 11 respondents did not state the highest school grade completed. However, from those who answered this question, the highest grade completed was 16 while lowest grade was 1

### Part III

#### Table 5: Family Income

From table 5, the highest and lowest family income prior month was \$6, 593 and \$0 respectively. The mean family income in the previous month was \$1,172.59 with a standard deviation of \$788.153. The data on family income was positively skewed. Out of 1000 respondents selected for the study, only 895 revealed their family income.

#### Graph III: Frequency Distribution for Family Income

From Graph III, most people had family income between \$ 0 and \$2,000. The data on family income is positively skewed with a mean of 1,172.59 and a standard deviation of \$788.153.

### Conclusion

Descriptive statistics help researchers to understand the nature of the data and to summarize it in a way that is easy to understand. From the descriptive analysis, a total of 1000 respondents were involved in the study, the maximum age of the respondents was 49.43 while the minimum age was 19.38. The mean family income in the previous month was \$1,172.59 with a standard deviation of \$788.153 and the data was positively skewed.

### Reference

Haden, P. (2019). Descriptive statistics. The Cambridge Handbook of Computing Education Research, 102-131.