According to Salkind and Rasmussen (2007) in any research it is always advisable to analyze the data collected from the study. As such this paper seeks to offer a descriptive statistics and interpretation for the study carried out to establish the relationship between a new bottling machine and the hours of the day. In analyzing these data, the study takes into consideration a number of interpretation phases as well statistical measures to establish the spread of the data and data correlation (Salkind & Rasmussen, 2007). For the interpretation phases, the study considers the use of measures of central tendency in establishing the typical score of the data set collected from the study. The descriptive statistics on the other hand took into consideration the measures of dispersion, the confidence level of the data population as well as the mode of data distribution.

### Interpretation Phrases

Measure of central tendency: is a type of descriptive statistic that allows the researcher to establish the average as well as the typical score in a set of data. In this case, the measures of central tendency were calculated and recorded in a table under the descriptive statistics for weight of the bottle and sample.

Mean; the mean was calculated as the average of the given data for both the weight as well as the number of hours.

ii. Median; for this project the distribution was taken to be normal. Therefore, the median was calculated as the point whereby any data set above or below this data point accounts for 50% of the total distribution.

Mode; the modal value for this study was the one that was more frequent within the data set for the sample and the weight.

### Measures of Dispersion

The measures of dispersion are any form of indices for a given data showing the spread of the data set (Salkind & Rasmussen, 2007). The dispersion of data for this case was assessed using measures such as the inter-quartile range, standard deviation, quartile deviation, variance as well as the range. The Inter-quartile range which is commonly denoted as IQR was calculated by working out the difference between the upper percentile and the lower percentile of the given data set. The range of the data set was worked out through establishing the difference between the maximum and minimum score.

Range = the difference between the largest and smallest value of the data

### Confidence Interval

The confidence interval for this data set was worked out from a 95% confidence level since the data distribution was normal.With a 95% confidence level, the average of the population was between 9.844383 and 10.155491 for the weight and 11.724752 and 14.275248 for the sample.

### Data Distribution

The results from the study indicated a normal distribution. The study observed that 50% of the data total scores were under the average value for the weight as well as the data for the number of hours. In addition most of the data scores were nearer to the mean.

### Descriptive Statistics

**Bottle Weight **

Measure of Central Tendency: |
Mean = 9.999937 |

Measure of Dispersion: |
Standard deviation = 0.890876 |

Count: |
126 |

Minimum Maximum: |
9.9883 10.0135 |

Confidence Interval: |
9.844383 to 10.155491 |

The scatter below shows a plot of the descriptive statics for the weight of the bottle and the sample number of hours.

### Sample

The data distribution is normal

Central Tendency: |
Median = 13 |

Measure of Dispersion: |
Inter-quartile Range = ± 12 |

Count: |
126 |

Minimum Maximum: |
24 25 |

Confidence Interval: |
11.724752 to 14.275248 |

### Interpretation of the Descriptive Statistics

**Weight of the Bottle**

For the study, a total of 126 units were selected on a random basis. The weight of each individual unit was observed to fall within 9.9883 and 10.0135. However, on average the weight was 9.999937. About 50% of the bottle’s weight was above 9.999937 but had a variation of +/- 0.155554. From the given data, it was evident that the average weight on a 95% basis was between 9.844383 and 10.155491.

**Sample**

The data collected for the study was normally distributed with one hundred and twenty six units under investigation. The range for the sample data was between 1 and 25. However, on average the sample unit was 13. About 50% of the bottle’s weight was above 13 but had a variation of +/- 0.1275248.

From the given population, it was evident that the average on a 95% confidence level basis

Descriptive Statistics |
WEIGHT |
SAMPLE |

Count Mean Sample standard deviation Sample variance Minimum Maximum Range Confidence interval 95% lower Confidence interval 95% upper Half-width 1 Median 3 Mode Low extremes Low outliers High outliers High extremes |
126 9.999937 0.890876 0.793660486 9.9883 10.0135 0.0252 9.844383 10.155491 0.155554 9.9966 9.9998 10.0027 10.0032 0 0 0 0 |
126 13 7.303511 53.34126984 1 25 24 11.724752 14.275248 1.275248 7 13 19 1 0 0 0 0 |

was between 11.724752 and 14.275248. The most frequent unit for the population was 1.

Scatter plot for Weight versus sample number of hours

#### References

- Salkind, N., & Rasmussen, K. (2007).
*Encyclopedia of measurement and statistics*. Thousand Oaks, Calif.: SAGE Publications.