A city in the Pacific Northwest recorded its highest temperature at 91 degrees Fahrenheit and its lowest temperature at 12 degrees Fahrenheit for a particular year. Use this information to find the upper and lower limits of the first class if you wish to construct a frequency distribution with 10 classes.

The lower limit of the first class is always going to be the lowest value. The lowest temperature at 12 degrees Fahrenheit for a particular year. So the lower limit is going to be 12 degrees Fahrenheit.

To find the upper limit of the first class we have to first find the length of each class.

This is the highest temperature subtracted by the lowest, and divided by the number of classes.

91 - 12 = 79

10 classes

79/10 = 7.9 rounded up to 8.

So the upper limit will be 8 added to 12, 8+12 = 20.

MrRoyal MrRoyal · Answer 2 · 2021-10-15T14:57:05+02:00

The limits of a frequency distribution is the range of value in each class.

The lower and the upper limits of the first class are 12 and 20, respectively.

The given parameters are:

[tex]Maximum = 91[/tex]

[tex]Minimum = 12[/tex]

[tex]n = 10[/tex]

First, we calculate the range of the distribution

[tex]Range = Maximum - Minimum[/tex]

[tex]Range = 91 - 12[/tex]

[tex]Range = 79[/tex]

Calculate the class width using:

[tex]Width = \frac{Range}n[/tex]

So, we have:

[tex]Width = \frac{79}{10}[/tex]

[tex]Width = 7.9[/tex]

Approximate

[tex]Width = 8[/tex]

The minimum value of the distribution can be used as the lower limit.

i.e.

[tex]Lower = 12[/tex]

The upper limit is calculated using

[tex]Upper = Lower + Width[/tex]

[tex]Upper = 12 +8[/tex]

[tex]Upper = 20[/tex]

Hence, the lower and the upper limits of the first class are 12 and 20, respectively.

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