A student's grades in a history class are shown in the histogram.

Question

The histogram is titled Grades in History Class, and the x-axis is labeled Grade Earned. The x-axis has intervals of 41 to 50, 51 to 60, 61 to 70, 71 to 80, 81 to 90, and 91 to 100. The y-axis is labeled Frequency and starts at 0 with tick marks every one unit up to 10. There is a shaded bar above 41 to 50 that stops at 2, above 51 to 60 that stops at 1, above 61 to 70 that stops at 1, above 71 to 80 that stops at 4, above 81 to 90 that stops at 7, and above 91 to 100 that stops at 6.

Which statement best describes the spread and distribution of the data?

The data is almost symmetric, with a maximum range of 59. This might be because the topic is easily understood by the students.
The data is skewed, with a maximum range of 59. This might be because the teacher offered extra credit, and most of the students did that to increase their grades above 70.
The data is bimodal, with a maximum range of 59. This might be because students either did not understand and earned less than 51, or they knew the topic well and earned higher than 90.
The data is symmetric, with a maximum range of 59. This might be because the topic was very difficult for the students and most of them earned lower grades.

Answer 1

To best describe the spread and distribution of the data based on the histogram provided, let's analyze the key characteristics:

1. Distribution Shape:

   • The frequencies of grades show that there are very few low scores (2 students scored between 41-50, 1 scored between 51-60, and 1 scored between 61-70).
   • The majority of students scored higher, with 4 in the 71-80 range, 7 in the 81-90 range, and 6 in the 91-100 range. This creates a distribution with a substantial concentration of grades in the higher ranges, indicating a skew to the left (or positively skewed).

2. Maximum Range:

   • The range of the grades is from 41 to 100, which gives a maximum range of 100 - 41 = 59.

3. Conclusions:

   • Considering the description that the grades are not evenly distributed but tend to cluster at the higher end suggests it is skewed rather than symmetric, bimodal, or symmetric with a maximum range.

Given this analysis, the best statement that describes the spread and distribution of the data is:

The data is skewed, with a maximum range of 59. This might be because the teacher offered extra credit, and most of the students did that to increase their grades above 70.

This option aligns with the observed distribution of grades in the histogram.