Probiotics are foods that supply beneficial bacteria which ease bloating, intestinal gas, may help fight off colds, and improve heart health. A survey of the probiotic preferences of sixteen people was conducted with the results shown in the table below.

kimchi | kimchi | kimchi | sakau |

kimchi | kimchi | daikon | sakau |

kimchi | kimchi | daikon | sakau |

kimchi | kimchi | daikon | miso |

- ____________________ What is the level of measurement?
- n = __________ What is the sample size n?
- mode = ____________________ What is the mode?

Bacterium | CFU/mL 10⁴ |
---|---|

Clostridium perfringens | 4.3 |

Staphylococcus aureus | 2.9 |

Salmonella typhimurium | 3.6 |

Listeria monocytogenes | 6.3 |

Vibrio parahaemolyticus | 2.0 |

Escherichia coli | 5.2 |

Lactobacillus kimchii | 22.0 |

Bacillus cereus | 6.4 |

According to a study of kimchi reported in Importance of lactic acid bacteria in Asian fermented foods, kimchi starts with the presence of many harmful pathogens. After seven days of fermentation, all of the harmful bacteria have been killed off by the beneficial (good) lactobacillus bacteria usch as L. kimchii. When ingested, L. kimchii has a similar effect in the intestines, killing off harmful bacteria. The table is loosely based on the reported bacteria levels at the start of the kimchi fermentation process. Use the numbers in the CFU/mL 10⁴ column to make the following calculations.

- ____________________ What is the level of measurement?
- n= __________ Calculate the sample size n.
- Q0 = __________ Calculate the minimum (zeroth quartile).
- Q1 = __________ Calculate the first quartile.
- Q2 = __________ Calculate the median (second quartile).
- Q3 = __________ Calculate the third quartile.
- Q4 = __________ Calculate the maximum (fourth quartile).
- IQR = __________ Calculate the Inter-Quartile Range.
- Make a sketch of the box plot for this time data.
- x = __________ Calculate the sample mean x.
- mode = __________ Calculate the mode.
- sx = __________ Calculate the sample standard deviation sx.
- CV = __________ Calculate the sample coeficient of variation CV.
- z = __________ Calculate the z-score for 22.
- range = __________ Calculate the range.
- width = __________ If the time data is divided into
**five**classes, what is the width of a single class? -
Determine the frequency and calculate the relative frequency for the data.
Record your results in the table provided.

Class upper limits Frequency F Rel. Freq. **Sums:** -
Sketch a
**frequency**histogram for the data, labeling your horizontal axis and vertical axis as appropriate. - What is the shape of the histogram?

*Homemade kimchi is the best! Kimchi photograph courtesy of Gangnam Street Restaurant lunch buffett, Nett, Pohnpei.*