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You recorded the minimum temperatures per day for the past month. The results are as follows: Group the data in six groups (six categories) and complete.

Mathematics

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Step-by-step solution

4 steps

  1. Identify the data points and determine the range.

    The given minimum temperatures are:
    12∘C,13∘C,9∘C,10∘C,11∘C,12∘C,11∘C,7∘C,11∘C,10∘C12^\circ\text{C}, 13^\circ\text{C}, 9^\circ\text{C}, 10^\circ\text{C}, 11^\circ\text{C}, 12^\circ\text{C}, 11^\circ\text{C}, 7^\circ\text{C}, 11^\circ\text{C}, 10^\circ\text{C}
    10∘C,7∘C,8∘C,12∘C,8∘C,13∘C,8∘C,9∘C,9∘C,9∘C10^\circ\text{C}, 7^\circ\text{C}, 8^\circ\text{C}, 12^\circ\text{C}, 8^\circ\text{C}, 13^\circ\text{C}, 8^\circ\text{C}, 9^\circ\text{C}, 9^\circ\text{C}, 9^\circ\text{C}
    10∘C,12∘C,10∘C,11∘C,7∘C,11∘C,7∘C,13∘C,9∘C,10∘C10^\circ\text{C}, 12^\circ\text{C}, 10^\circ\text{C}, 11^\circ\text{C}, 7^\circ\text{C}, 11^\circ\text{C}, 7^\circ\text{C}, 13^\circ\text{C}, 9^\circ\text{C}, 10^\circ\text{C}
    10∘C,12∘C10^\circ\text{C}, 12^\circ\text{C}
    There are 32 data points in total.
    The minimum temperature is 7∘C7^\circ\text{C}.
    The maximum temperature is 13∘C13^\circ\text{C}.
    The range is 13∘C−7∘C=6∘C13^\circ\text{C} - 7^\circ\text{C} = 6^\circ\text{C}.

  2. Define the six categories.

    Since the range is 6∘C6^\circ\text{C} and we need six categories, we can define categories with a width of 1∘C1^\circ\text{C}. However, this would result in 7 distinct temperature values (7,8,9,10,11,12,137, 8, 9, 10, 11, 12, 13). To fit into exactly six categories, we will group the highest two temperatures together.
    The categories are:

    • 7∘C7^\circ\text{C}
    • 8∘C8^\circ\text{C}
    • 9∘C9^\circ\text{C}
    • 10∘C10^\circ\text{C}
    • 11∘C11^\circ\text{C}
    • 12∘C−13∘C12^\circ\text{C} - 13^\circ\text{C}

  3. Tally the frequencies for each category.

    • For 7∘C7^\circ\text{C}: Count occurrences of 7. 7,7,7,77, 7, 7, 7 (4 times)
    • For 8∘C8^\circ\text{C}: Count occurrences of 8. 8,8,88, 8, 8 (3 times)
    • For 9∘C9^\circ\text{C}: Count occurrences of 9. 9,9,9,9,99, 9, 9, 9, 9 (5 times)
    • For 10∘C10^\circ\text{C}: Count occurrences of 10. 10,10,10,10,10,10,1010, 10, 10, 10, 10, 10, 10 (7 times)
    • For 11∘C11^\circ\text{C}: Count occurrences of 11. 11,11,11,11,1111, 11, 11, 11, 11 (5 times)
    • For 12∘C−13∘C12^\circ\text{C} - 13^\circ\text{C}: Count occurrences of 12 and 13. 12,13,12,12,13,12,13,1212, 13, 12, 12, 13, 12, 13, 12 (8 times)

  4. Complete the frequency distribution table.

    The total frequency is 4+3+5+7+5+8=324 + 3 + 5 + 7 + 5 + 8 = 32, which matches the total number of data points.

    Minimum Temperature categories (∘C)TalliesFrequency7∣∣∣∣48∣∣∣39∣∣∣∣ |510∣∣∣∣ ||711∣∣∣∣ |512−13∣∣∣∣ ||||8\begin{array}{|l|l|l|} \hline \text{Minimum Temperature categories } (^\circ\text{C}) & \text{Tallies} & \text{Frequency} \\ \hline 7 & |||| & 4 \\ \hline 8 & ||| & 3 \\ \hline 9 & |||| \text{ |} & 5 \\ \hline 10 & |||| \text{ ||} & 7 \\ \hline 11 & |||| \text{ |} & 5 \\ \hline 12 - 13 & |||| \text{ ||||} & 8 \\ \hline \end{array}
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