Question
9.24 Qulz: Population Genetics This graph shows the heights of 5014-year-old female students. Heights were recorded to the nearest centimeter (cm) Heights of Female Students 30 25 so 20 15 10 5 0 151-154 155-158 159-162 163-166 167-170 Height (cm) What approximate range of heights represents the middle 48% of 14-year-old female students? A. 155 cm -166 cm B. 151 cm-170 cm C. 159 cm -162 cm D. 155 cm -158 cm
Answer
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Rona
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Answer
To find the range of heights that represents the middle 48% of the 14-year-old female students, we need to look for the range that includes the central 48% of the data. This is similar to finding the interquartile range, which includes the middle 50% of the data. Since the options given are ranges, we will look for the range that most closely includes the middle 48% of the students.First, let's calculate the total number of students:5 (151-154 cm) + 10 (155-158 cm) + 20 (159-162 cm) + 25 (163-166 cm) + 5 (167-170 cm) = 5 + 10 + 20 + 25 + 5 = 65 studentsNow, we want to find the middle 48% of these 65 students. To do this, we calculate 48% of 65:48% of 65 = 0.48 * 65 ≈ 31.2Since we can't have a fraction of a student, we'll consider approximately 31 students to represent the middle 48%.Next, we need to find the range that includes these 31 students. We start from the middle of the distribution and work outwards. The largest group is the 163-166 cm range with 25 students. To include more students to get close to 31, we should include the next largest group adjacent to this one.The 159-162 cm range has 20 students. If we add this to the 25 students in the 163-166 cm range, we get:25 (163-166 cm) + 20 (159-162 cm) = 45 studentsThis is more than 31, so we've included too many students. However, since we're looking for the approximate range and we can't include part of a group, we'll need to include the entire group. Therefore, we should not include all of the 159-162 cm range to represent the middle 48%.The next largest group is the 155-158 cm range with 10 students. If we add this to the 25 students in the 163-166 cm range, we get:25 (163-166 cm) + 10 (155-158 cm) = 35 studentsThis is closer to the 31 students we're aiming for. Since we can't include part of a group and we need to find the best approximation, the range of 155 cm to 166 cm is the closest we can get to representing the middle 48% of the students.Therefore, the answer is:A. 155 cm - 166 cm