Question

the table below shows the scores of a group of students on a 10 - point quiz. the mean score on this test is: the median score on this test is: test score 3 4 5 6 7 8 9 10 frequency 5 1 3 1 1 3 0 2 question help: video 1 video 2 message instructor submit question

Explanation:

Step1: Calculate the total number of students

$2 + 0+3 + 1+1 + 3+1 + 5=16$

Step2: Calculate the sum of all scores

$(10\times2)+(9\times0)+(8\times3)+(7\times1)+(6\times1)+(5\times3)+(4\times1)+(3\times5)=20 + 0+24 + 7+6 + 15+4 + 15=91$

Step3: Calculate the mean

The mean $\bar{x}=\frac{\text{Sum of scores}}{\text{Total number of students}}=\frac{91}{16}=5.6875$

Step4: Find the median

Since there are $n = 16$ (an even - numbered data set), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered data values. First, list out the data set by frequency: 3,3,3,3,3,4,5,5,5,6,7,8,8,8,10,10. The 8th and 9th values are 5 and 5. The median $M=\frac{5 + 5}{2}=5$

Answer:

The mean score is $5.6875$ and the median score is $5$