Question

question #3
what is the median score achieved by a student who received the following scores on 10 math quizzes?
68 66 70 62 71 58 81 82 63 79

83
69
85
82

question #4
which data set has a mean of 59, median of 62, and a mode of 75?
11 33 22 88 67 54 75 75 62 59 59
30 90 62 37 75 53 42 48 62 75 75
42 50 22 19 59 66 62 47 78 74 75
10 29 33 20 11 55 74 75 75 22 22

Explanation:

Step1: Arrange scores in ascending order for Question #3

58, 62, 63, 66, 68, 70, 71, 79, 81, 82

Step2: Calculate median for Question #3

Since there are 10 (an even - numbered) data points, the median is the average of the 5th and 6th ordered values. So, $\frac{68 + 70}{2}=69$

Step3: Check mean, median and mode for Question #4

For the first option of Question #4:
Mean: $\frac{11 + 33+22 + 88+67+54+75+75+62+59+59}{11}=\frac{635}{11}\approx57.73$
Median (after arranging in ascending order: 11, 22, 33, 54, 59, 59, 62, 67, 75, 75, 88) is 59
Mode is 59 and 75

For the second option of Question #4:
Mean: $\frac{30 + 90+62+37+75+53+42+48+62+75+75}{11}=\frac{659}{11}\approx59.91$
Median (after arranging in ascending order: 30, 37, 42, 48, 53, 62, 62, 75, 75, 75, 90) is 62
Mode is 75

For the third option of Question #4:
Mean: $\frac{42+50+22+19+59+66+62+47+78+74+75}{11}=\frac{634}{11}\approx57.64$
Median (after arranging in ascending order: 19, 22, 42, 47, 50, 59, 62, 66, 74, 75, 78) is 59
Mode is 75

For the fourth option of Question #4:
Mean: $\frac{10+29+33+20+11+55+74+75+75+22+22}{11}=\frac{426}{11}\approx38.73$
Median (after arranging in ascending order: 10, 11, 20, 22, 22, 29, 33, 55, 74, 75, 75) is 29
Mode is 22 and 75

The second option for Question #4 has a mean of approximately 59, median of 62 and mode of 75

Answer:

Question #3: B. 69
Question #4: B. 30, 90, 62, 37, 75, 53, 42, 48, 62, 75, 75