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.

a. given: 4, 4, 3, 9, 5; mean: 5; median: 4; mode: 4
(handwritten: 25 ÷ 5 = 5)

b. given: 8, 4, 5, 8, 5, 4, 8; mean: 6; median: 5; mode: 8

c. given: 10, 13, 11, 13, 13; mean: 12; median: 13; mode: 13

d. given: 5, 12, 13, 16, 12, 14, 12, 5, 10; mean: 11; median: 12; mode: 12

e. given: 15, 18, 19, 20, 22, 24, 22; mean: 20; median: 20; mode: 22

f. given: 42, 34, 36, 24, 34; mean: 34; median: 34; mode: 34

Explanation:

Step 1: Analyze Set a (4, 4, 3, 9, 5)

• Mean: Sum the numbers: \(4 + 4 + 3 + 9 + 5 = 25\). Divide by the count (\(5\)): \(\frac{25}{5} = 5\).
• Median: Sort the numbers: \(3, 4, 4, 5, 9\). The middle number is \(4\).
• Mode: The number that appears most often is \(4\) (appears twice).

Step 2: Analyze Set b (8, 4, 5, 8, 5, 4, 8)

• Mean: Sum: \(8 + 4 + 5 + 8 + 5 + 4 + 8 = 42\). Divide by \(7\): \(\frac{42}{7} = 6\).
• Median: Sort: \(4, 4, 5, 5, 8, 8, 8\). Middle number is \(5\).
• Mode: \(8\) (appears three times).

Step 3: Analyze Set c (10, 13, 11, 13, 13)

• Mean: Sum: \(10 + 13 + 11 + 13 + 13 = 60\). Divide by \(5\): \(\frac{60}{5} = 12\).
• Median: Sort: \(10, 11, 13, 13, 13\). Middle number is \(13\).
• Mode: \(13\) (appears three times).

Step 4: Analyze Set d (5, 12, 13, 16, 12, 14, 12, 5, 10)

• Mean: Sum: \(5 + 12 + 13 + 16 + 12 + 14 + 12 + 5 + 10 = 99\). Divide by \(9\): \(\frac{99}{9} = 11\).
• Median: Sort: \(5, 5, 10, 12, 12, 12, 13, 14, 16\). Middle number is \(12\).
• Mode: \(12\) (appears three times).

Step 5: Analyze Set e (15, 18, 19, 20, 22, 24, 22)

• Mean: Sum: \(15 + 18 + 19 + 20 + 22 + 24 + 22 = 140\). Divide by \(7\): \(\frac{140}{7} = 20\).
• Median: Sort: \(15, 18, 19, 20, 22, 22, 24\). Middle number is \(20\).
• Mode: \(22\) (appears twice).

Step 6: Analyze Set f (42, 34, 36, 24, 34)

• Mean: Sum: \(42 + 34 + 36 + 24 + 34 = 170\). Divide by \(5\): \(\frac{170}{5} = 34\).
• Median: Sort: \(24, 34, 34, 36, 42\). Middle number is \(34\).
• Mode: \(34\) (appears twice).

Answer:

Given Set	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