Question

averages: mean, median & mode
data and graphing worksheet
find the mean, median and mode for each set of numbers. show your work and write your answer in the space provided.

given	mean	median	mode
b. 8, 4, 5, 8, 5, 4, 8
c. 10, 13, 11, 13, 13
d. 5, 12, 13, 16, 12, 14, 12, 5, 10
e. 15, 18, 19, 20, 22, 24, 22
f. 42, 34, 36, 24, 34

Explanation:

Step1: Calculate mean formula

Mean = $\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $x_{i}$ are data - points and $n$ is the number of data - points.

Step2: Find median

Arrange data in ascending order. If $n$ is odd, median is the middle - value. If $n$ is even, median is the average of the two middle - values.

Step3: Find mode

Mode is the value that appears most frequently in the data set.

a. For the data set 4, 4, 3, 9, 5

• Mean:
• $\sum_{i = 1}^{5}x_{i}=4 + 4+3 + 9+5=25$
• $n = 5$
• Mean=$\frac{25}{5}=5$
• Median:
• Arrange in ascending order: 3, 4, 4, 5, 9
• $n = 5$ (odd), so median = 4
• Mode: 4 (appears twice)

b. For the data set 8, 4, 5, 8, 5, 4, 8

• Mean:
• $\sum_{i = 1}^{7}x_{i}=8 + 4+5 + 8+5 + 4+8=42$
• $n = 7$
• Mean=$\frac{42}{7}=6$
• Median:
• Arrange in ascending order: 4, 4, 5, 5, 8, 8, 8
• $n = 7$ (odd), so median = 5
• Mode: 8 (appears three times)

c. For the data set 10, 13, 11, 13, 13

• Mean:
• $\sum_{i = 1}^{5}x_{i}=10 + 13+11 + 13+13=60$
• $n = 5$
• Mean=$\frac{60}{5}=12$
• Median:
• Arrange in ascending order: 10, 11, 13, 13, 13
• $n = 5$ (odd), so median = 13
• Mode: 13 (appears three times)

d. For the data set 5, 12, 13, 16, 12, 14, 12, 5, 10

• Mean:
• $\sum_{i = 1}^{9}x_{i}=5 + 12+13 + 16+12 + 14+12 + 5+10=99$
• $n = 9$
• Mean=$\frac{99}{9}=11$
• Median:
• Arrange in ascending order: 5, 5, 10, 12, 12, 12, 13, 14, 16
• $n = 9$ (odd), so median = 12
• Mode: 12 (appears three times)

e. For the data set 15, 18, 19, 20, 22, 24, 22

• Mean:
• $\sum_{i = 1}^{7}x_{i}=15 + 18+19 + 20+22 + 24+22=140$
• $n = 7$
• Mean=$\frac{140}{7}=20$
• Median:
• Arrange in ascending order: 15, 18, 19, 20, 22, 22, 24
• $n = 7$ (odd), so median = 20
• Mode: 22 (appears twice)

f. For the data set 42, 34, 36, 24, 34

• Mean:
• $\sum_{i = 1}^{5}x_{i}=42 + 34+36 + 24+34=170$
• $n = 5$
• Mean=$\frac{170}{5}=34$
• Median:
• Arrange in ascending order: 24, 34, 34, 36, 42
• $n = 5$ (odd), so median = 34
• Mode: 34 (appears twice)

Answer:

Given	Mean	Median	Mode
8, 4, 5, 8, 5, 4, 8	6	5	8
10, 13, 11, 13, 13	12	13	13
5, 12, 13, 16, 12, 14, 12, 5, 10	11	12	12
15, 18, 19, 20, 22, 24, 22	20	20	22
42, 34, 36, 24, 34	34	34	34