Data Driven Statistics

[Name of Student]

[Name of the Institution]

Data Driven Statistics

Introduction

The purpose of this paper is to analyze and interpret the data representing members of the gym. The analysis in this paper aims to explore the data representing gym members in light of diverse statistical tests and approaches. There are diverse outcomes to be drawn from the data comprising two study variables 'body fat' and 'weight' of gym members. The owner of the gym is concerned about the influence of body fat on weight of gym members in order to prescribe effective dietary pattern along with workout plans to the members of gym. Therefore, the analysis in this paper is supposed to test several assumptions via the implication of diverse statistical tests in order to validate the outcomes.

Part I

Descriptive Statistics

In the first part of the analysis, the data representing members of gym was analyzed via the implication of descriptive statistics. The core objective of applying descriptive statistical technique on the data was to extract useful values representing the data. Descriptive analysis facilitates data presentation and interpretation. Hence, in this part of the paper descriptive statistics was applied on data representing gym members. According to the analysis of data as per the study variables selected, it can be stated that the mean value representing body fat is 18.9385, median was recorded as 19; nonetheless, majority of the gym members had 19% body fat.

In addition, the values representing standard deviation and variance of the data are 7.75086 and 60.076 respectively. While analyzing the data in terms of the study variable 'weight', it was observed that the mean and median values representing the data are 178.92 and 176.50 respectively. Nonetheless, the weight representing most of gym members was 152.25. In addition, 29.3892 and 863.723 are the values representing standard deviation and variance of data.

Statistics

Body Fat

Weight

N

Valid

252

252

Missing

0

0

Mean

18.9385

178.92

Median

19.0000

176.50

Mode

19.00a

152.25a

Std. Deviation

7.75086

29.3892

Variance

60.076

863.723

Range

45.10

244.65

Percentiles

25

12.8000

158.50

50

19.0000

176.50

75

24.6000

197.00

a. Multiple modes exist. The smallest value is shown

Part II

Hypotheses Testing

According to the assumption of Silver Gym's owner, the average body fat in men attending Silver's Gym is 20%. Nonetheless, it can be stated that this assumption is not validated. Therefore, there is significant possibility that the assumption of gym owner might be wrong. In order to check this assumption, a set of hypotheses were constructed in order to check the validity of assumption. In order to test the hypotheses, one sample t-test was adapted as statistical analysis measure to analyze the data and reveal the validity of analysis. The hypotheses constructed to validate the prescribed statement are enlightened below.

Ho: The average body fat in men attending Silver's Gym is not 20%.

H1: The average body fat in men attending Silver's Gym is 20%.

According to the implication of one sample t-test, following tables were extracted as outcome of representing data. On the basis of outcomes extracted through the implication of one sample t-test, the hypotheses are to be validated in order to reach appropriate conclusion. According to the implication of one sample t-test, it can be stated that the mean value representing the body fat in men attending Silver's Gym is ...