Constructing a Frequency Distribution and a Frequency Histogram

In Exercises 31–34, construct a frequency distribution and a frequency histogram for the data set using the indicated number of classes. Describe any patterns.

Pepper Pungencies

Number of classes: 5

Data set: Pungencies (in thousands of Scoville units) of 24 tabasco peppers

Problem 32E

Constructing a Frequency Distribution and a Frequency Histogram In Exercise, construct a frequency distribution and a frequency histogram for the data set using the indicated number of classes. Describe any patterns.

Pepper Pungencies

Number of classes: 5

Data set: Pungencies (in thousands of Scoville units) of 24 tabasco peppers

35 |
51 |
44 |
42 |
37 |
38 |
36 |
39 |

44 |
43 |
40 |
40 |
32 |
39 |
41 |
38 |

42 |
39 |
40 |
46 |
37 |
35 |
41 |
39 |

Step by Step Solution

Step 1 of 3

The number of classes stated in the problem = 5

The minimum data entry is 32 and the maximum data entry is 51, so the range is

Range = 51 - 32 = 19.

Divide the range by the number of classes and round up to find the class width, ie;

Class width =

Round up to the next convenient number, 4.

The minimum data entry is 32 and add the class width of 4 to the lower limit of each previous class to get the lower limits of the remaining four classes.

We have the upper limit of the first class as 35. Then the first class is 32 - 35. The upper limit of the first class, 35 is one less than the lower limit of the second class. Then add the class width of 4 to the upper limit of each previous class to get the upper limits of the remaining four classes. In this way we can write each class, as shown below,

Lower limit |
Upper limit |

32 |
35 |

36 |
39 |

40 |
43 |

44 |
47 |

48 |
51 |

So, we have the lower and upper limit of each class. Now we can construct a frequency distribution.

A frequency distribution is a table that shows classes or intervals of data entries with a count of the number of entries in each class. The frequency f of a class is the number of data entries in the class. The frequency distribution of the above data set is shown below,

Class |
Frequency, f |

32-35 |
3 |

36-39 |
9 |

40-43 |
8 |

44-47 |
3 |

48-51 |
1 |