Question

Suppose Professor Miller obtained the following results on the 1st Physics Test this semester Grades on the 1t Physics Test 72 Physics Test Grade 7 2 9 1 2 4 6 7 355 6 5 6 05689 00000 1 33344556778 8 8 8999 7 8 0012233356667888999 0000 1 1 2333333556668 10 00 1. Determine the mean, median, mode, and range for the grade distribution of the Physics Test. Mean: Median: Mode: Range: 2. Determine the 5-Number summary and make a box-and-whiskers plot for the data. Include the box-and-whiskers plot in your response. <Compose answer here> 3. What does the box-and-whiskers plot tell you about the shape of the distribution? <Compose answer here>

Answer 1

Solution: Given that samples :
19,46,47,53,55,55,56,60,65,66,68,69,70,70,70,70,70,71,73,73,73,74,74,75,75,76,77,77,78,78,78,78,79,79,79,80,80,81,82,82,83,83,83,85,86,86,86,87,88,88,88,89,89,89,90,90,90,90,91,91,92,93,93,93,93,93,93,95,95,96,96,96,98,100,100

1.
mean : sum of terms/number of terms = 5959/75 = 79.4533
median : 81
=> The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.
mode : 93
=> The mode of a set of data is the value in the set that occurs most often.

2. 5-Number summary :
Minimum : 19
Quartile Q1: 73
Median : 81
Quartile Q3: 90
Maximum : 100

3. box-and-whiskers plot :

Box-Plot Graph: 100Maximum Third Quartile 90 81 Median First Quartile 73 47 Minimum 19

=>  symmetric distribution