# Investigating the Statistical Distribution of Learning Coverage in MOOCs

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## Abstract

**:**

## 1. Introduction

## 2. Related Work

#### 2.1. MOOC Learning Behavior

#### 2.2. Zipf’s Law

## 3. Dataset and Methods

#### 3.1. Dataset

#### 3.2. Learning Coverage

#### 3.3. Fitting Zipf’s Law

#### 3.4. Goodness-of-fit Test

${H}_{0}$: The data of learning coverage is consistent |

with a Zipf distribution with parameter $\widehat{\alpha}$. |

## 4. Results

`fminunc`, as the optimization solver with the initial $\alpha $ set to be 1.5. After obtaining $\widehat{\alpha}$, we conduct a chi-square test to determine whether the observed data fit with the Zipf’s law. The procedure above is conducted for all 92 courses.

## 5. Discussion

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Registrants and participants distribution: (

**a**) Registrants distribution; (

**b**) Participants distribution.

**Figure 5.**Linear regression results: (

**a**) The exponent parameter $\alpha $; (

**b**) The R-squared values.

**Figure 6.**Maximum likelihood estimation (MLE) fitting results. (

**a**) Medical Parasitology in the xuetangX dataset; (

**b**) Mechanics Review in the edX dataset.

Statistics | xuetangX Dataset | edX Dataset | ||
---|---|---|---|---|

$\mathit{\alpha}$ | p-Value | $\mathit{\alpha}$ | p-Value | |

Mean | 1.3068 | 0.3707 | 1.4268 | 0.0000 |

Min. | 0.8915 | 0.0000 | 1.2352 | 0.0000 |

1Q | 1.2107 | 0.0000 | 1.2898 | 0.0000 |

Median | 1.2998 | 0.1863 | 1.4222 | 0.0000 |

3Q | 1.3709 | 0.8420 | 1.5296 | 0.0000 |

Max. | 1.9751 | 1.0000 | 1.6860 | 0.0000 |

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**MDPI and ACS Style**

Li, X.; Men, C.; Du, Z.; Liu, J.; Li, M.; Zhang, X.
Investigating the Statistical Distribution of Learning Coverage in MOOCs. *Information* **2017**, *8*, 150.
https://doi.org/10.3390/info8040150

**AMA Style**

Li X, Men C, Du Z, Liu J, Li M, Zhang X.
Investigating the Statistical Distribution of Learning Coverage in MOOCs. *Information*. 2017; 8(4):150.
https://doi.org/10.3390/info8040150

**Chicago/Turabian Style**

Li, Xiu, Chang Men, Zhihui Du, Jason Liu, Manli Li, and Xiaolei Zhang.
2017. "Investigating the Statistical Distribution of Learning Coverage in MOOCs" *Information* 8, no. 4: 150.
https://doi.org/10.3390/info8040150