Median and Mode

Show your work for each problem.

1.
What is the median of: ?
1. a)
2. b)
3. c)
4. d)
Answer:
With 5 values in order, the median is the 3rd value: . The median is .
2.
What is the mode of: ?
1. a)
2. b)
3. c)
4. d)
Answer:
Count each value: appears once, appears twice, appears once, appears once. The mode is .
3.
Find the median of:
Answer: 6
Ordered: . The middle (3rd) value is .
4.
Find the mode of:
Answer: 5
appears 3 times, more than any other value. The mode is .
5.
Find the median of:
Answer: 11
1. First, order the numbers from least to greatest. What is the smallest number? 7
2. What is the complete ordered list? 7, 9, 11, 12, 15
3. How many values are there? 5
4. Since there are 5 values (odd), which position is the median? 3
5. What is the 3rd value in the ordered list? 11
6.
What is the median of: ?
1. a)
2. b)
3. c)
4. d)
Answer:
With 4 values, the middle two are and . Median = .
7.
The data set has:
1. a)mode =
2. b)mode =
3. c)no mode
4. d)mode =
Answer: no mode
Each value appears exactly once. When no value appears more than others, there is no mode.
8.
Find the median of:
Answer: 6
Ordered: . Middle values are and . Median = .
9.
What is the mode of: ?
Answer: 8
appears 2 times, appears 1 time, appears 1 time, appears 3 times. The mode is .
10.
Find the median of:
Answer: 22.5
1. Order the numbers from least to greatest: 10, 15, 20, 25, 30, 35
2. How many values are there? 6
3. Is this odd or even? even
4. What are the two middle values (3rd and 4th)? 20 and 25
5. What is their average? 22.5
11.
A dataset has values: . Find both the median and mode.
Answer: median: 8, modes: 6 and 8
1. Is the data already in order? yes
2. How many values are there? 5
3. What is the median (middle value)? 8
4. How many times does 6 appear? 2
5. How many times does 8 appear? 2
6. What are the modes? 6 and 8
12.
Test scores: . Which statement is true?
1. a)Median = , mode =
2. b)Median = , no mode
3. c)Median = , mode =
4. d)Median = , no mode
Answer: Median = , no mode
With 7 ordered values, the median is the 4th: . Every score appears once, so there is no mode.
13.
Salaries (in thousands): . What is the median salary?
Answer: 45
With 7 values in order, the median is the 4th value: thousand. Note how the median () is more representative than the mean would be (distorted by ).
14.
Data: . Find the median and identify all modes.
Answer: median: 19, modes: 15 and 22
1. How many values are in the dataset? 8
2. Since 8 is even, which two positions are in the middle? 4th and 5th
3. What are the 4th and 5th values? 18 and 20
4. What is the median (average of 18 and 20)? 19
5. Which values appear more than once? 15 and 22
6. How many times do 15 and 22 each appear? 2 times each
7. What are the modes? 15 and 22
15.
Basketball points: . Find the mean, median, and mode. Which best represents typical performance?
Answer: mean: about 18.7, median: 18, mode: 18; median or mode best represent typical performance
1. Calculate the sum of all values: 168
2. Calculate the mean (sum / 9): 18.67
3. With 9 values (odd), which position is the median? 5th
4. What is the 5th value (median)? 18
5. Which value appears most often? 18
6. How many times does 18 appear? 3
7. Which measure best represents typical performance? median or mode