Question

consider the exam scores for 59 students when 7 students scored between 90 and 100, 12 students scored between 80 and 89, 21 students scored between 70 and 79, and 19 students scored below 70 (with their scores spread out to a low of 40). complete parts a through d

a) what shape would you expect for the distribution?
a. the distribution would probably be symmetric because there are no obvious factors to indicate that there would be a higher or lower exam score for any student
b. the distribution would probably be left - skewed because the scores are more spread out on the left side of the mode
c. the distribution would probably be symmetric because the only scores were between 40 and 100
d. the distribution would probably be right - skewed because many of the students got scores of 90 or better, and very few got low scores

b) what variation would you expect in the distribution?
a. the variation would probably be moderate because there are no obvious reasons to expect an especially large or small amount of variation
b. the variation would probably be large because many students got scores between 70 and 89 but scores range from 40 to between 90 and 100, and so the data are not clustered
c. the variation would probably be small because all the students would tend to have nearly the same exam scores
d. the variation would probably be moderate because the number of students is not especially large or small

Explanation:

For part (i), we analyze the score distribution: 19 students scored below 70 (spread from 40), 21 between 70 - 79, 12 between 80 - 89, 7 between 90 - 100. The left - hand side (lower scores) has more spread out data (19 students over a range of 40 - 70) compared to the right - hand side. In a left - skewed distribution, the tail is on the left (lower values) and the scores are more spread out on the left side of the mode (the mode is likely in the 70 - 79 range as it has the most students). Option B correctly describes this as left - skewed. Option A is wrong as there is a spread on the left. Option C is wrong because the range of scores (40 - 100) and the spread on the left don't indicate symmetry. Option D is wrong as it describes a right - skewed distribution, but our data has more spread on the left.

For part (ii), we look at the variation. The scores range from 40 to 100, with 19 students below 70, 21 in 70 - 79, 12 in 80 - 89, and 7 in 90 - 100. The data is not clustered in a narrow range; it spans from 40 to 100, and while there is a cluster in 70 - 79, there are also significant numbers of students in other ranges (especially the 40 - 70 range with 19 students). So the variation is large because the scores are spread out from 40 to 100 and not just clustered in a small area. Option A is wrong as there is a large spread. Option C is wrong as students don't have nearly the same scores. Option D is wrong as the number of students doesn't determine variation; it's the spread of scores. So Option B is correct.

Answer:

i) B. The distribution would probably be left - skewed because the scores are more spread out on the left side of the mode
ii) B. The variation would probably be large because many students got scores between 70 and 79 but scores range from 40 to between 90 and 100, and so the data are not clustered