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\tmean\tmedian\tmode
a. 4, 4, 3, 9, 5
4 + 4+3+9+5 ÷5 = 5\t5\t5

b. 8, 4, 5, 8, 5, 4, 8
8+4+5+8+5+4+8\t6

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

Step2: Calculate 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: Calculate mode

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

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

• Mean: $\frac{4 + 4+3 + 9+5}{5}=\frac{25}{5}=5$
• Median: Arrange in ascending order: $3,4,4,5,9$. The middle value is $4$, so median $ = 4$.
• Mode: The number $4$ appears twice, more frequently than other numbers, so mode $ = 4$.

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

• Mean: $\frac{8 + 4+5 + 8+5 + 4+8}{7}=\frac{42}{7}=6$
• Median: Arrange in ascending order: $4,4,5,5,8,8,8$. The middle value is $5$, so median $ = 5$.
• Mode: The number $8$ appears three times, more frequently than other numbers, so mode $ = 8$.

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

• Mean: $\frac{10 + 13+11 + 13+13}{5}=\frac{60}{5}=12$
• Median: Arrange in ascending order: $10,11,13,13,13$. The middle value is $13$, so median $ = 13$.
• Mode: The number $13$ appears three times, more frequently than other numbers, so mode $ = 13$.

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

• Mean: $\frac{5+12 + 13+16+12+14+12+5+10}{9}=\frac{99}{9}=11$
• Median: Arrange in ascending order: $5,5,10,12,12,12,13,14,16$. The middle value is $12$, so median $ = 12$.
• Mode: The number $12$ appears three times, more frequently than other numbers, so mode $ = 12$.

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

• Mean: $\frac{15 + 18+19+20+22+24+22}{7}=\frac{140}{7}=20$
• Median: Arrange in ascending order: $15,18,19,20,22,22,24$. The middle value is $20$, so median $ = 20$.
• Mode: The number $22$ appears twice, more frequently than other numbers, so mode $ = 22$.

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

• Mean: $\frac{42+34 + 36+24+34}{5}=\frac{170}{5}=34$
• Median: Arrange in ascending order: $24,34,34,36,42$. The middle value is $34$, so median $ = 34$.
• Mode: The number $34$ appears twice, more frequently than other numbers, so mode $ = 34$.

Answer:

Given	Mean	Median	Mode
b. $8,4,5,8,5,4,8$	$6$	$5$	$8$
c. $10,13,11,13,13$	$12$	$13$	$13$
d. $5,12,13,16,12,14,12,5,10$	$11$	$12$	$12$
e. $15,18,19,20,22,24,22$	$20$	$20$	$22$
f. $42,34,36,24,34$	$34$	$34$	$34$