Question

exam results for 100 students are given below. for the given exam results, briefly describe the shape and variation of the distribution.
median = 75, mean = 75, low score = 60, high score = 90

describe the shape of the distribution. choose the correct answer below.
a. the distribution is right - skewed because the median is less than the mean.
b. the distribution is left - skewed because the median is less than the mean.
c. the distribution is left - skewed because the median is greater than the mean.
d. the distribution is symmetric because the median is equal to the mean.
e. the distribution is right - skewed because the median is greater than the mean.

the difference between the greatest and least scores is \\(\square\\), which is \\(\square\\) compared to the number of students.
(type an integer or a decimal)

Explanation:

Step1: Determine the shape of the distribution

In a symmetric distribution, the mean and median are equal. Here, median = 75 and mean = 75. So, the distribution is symmetric.

Step2: Calculate the range

The range is calculated as \(high - low\). Given \(high = 90\) and \(low=60\), then \(range=90 - 60=30\).

Answer:

D. The distribution is symmetric because the median is equal to the mean.
The difference between the greatest and least scores is \(30\), which is relatively small compared to the number of students.