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The histogram below shows the students scores for a quiz. (a) If a student scored 85, which bar will they be added to? (b) How many students scored less than 70? (c) Which two categories of scores will total one less than the most popular category?

Mathematics

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Answers

3 parts
a

80-89\text{80-89}

b
11
c

50-59 and 80-89\text{50-59 and 80-89}

Step-by-step solution

6 steps

Part a· 1 step

  1. Identify the score range for a student who scored 85.

    A score of 85 falls within the range of 80-89.
    The student will be added to the bar representing scores from 80-89\boxed{\text{80-89}}.

Part b11

  1. Identify the number of students in categories with scores less than 70.

    Scores less than 70 include the categories 50-59 and 60-69.

    • Students scoring 50-59: 6
    • Students scoring 60-69: 5

  2. Sum the number of students in these categories.

    Total students=6+5=11\text{Total students} = 6 + 5 = 11

    11\boxed{11} students scored less than 70.

Part c

50-59 and 80-89\text{50-59 and 80-89}

  1. Determine the most popular category and its frequency.

    The most popular category is 70-79, with 8 students.

  2. Calculate the target total frequency.

    One less than the most popular category is 8−1=78 - 1 = 7 students.

  3. Find two categories whose frequencies sum to the target total of 7.

    • Category 50-59 has 6 students.
    • Category 80-89 has 1 student.
    6+1=76 + 1 = 7

    The two categories are 50-59 and 80-89\boxed{\text{50-59 and 80-89}}.

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