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. 4, 4, 3, 9, 5

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:

Part a:

Step 1: Calculate Mean

Sum the numbers: \(4 + 4 + 3 + 9 + 5 = 25\). Divide by the count (5): \(\frac{25}{5}=5\).

Step 2: Find Median

Arrange in order: \(3, 4, 4, 5, 9\). The middle number (3rd) is \(4\).

Step 3: Determine Mode

The number that appears most often is \(4\) (appears twice).

Part b:

Step 1: Calculate Mean

Sum: \(8 + 4 + 5 + 8 + 5 + 4 + 8 = 42\). Divide by 7: \(\frac{42}{7}=6\).

Step 2: Find Median

Arrange: \(4, 4, 5, 5, 8, 8, 8\). Middle number (4th) is \(5\).

Step 3: Determine Mode

\(8\) appears 3 times, most frequent.

Part c:

Step 1: Calculate Mean

Sum: \(10 + 13 + 11 + 13 + 13 = 60\). Divide by 5: \(\frac{60}{5}=12\).

Step 2: Find Median

Arrange: \(10, 11, 13, 13, 13\). Middle number (3rd) is \(13\).

Step 3: Determine Mode

\(13\) appears 3 times, most frequent.

Part d:

Step 1: Calculate Mean

Sum: \(5 + 12 + 13 + 16 + 12 + 14 + 12 + 5 + 10 = 99\). Divide by 9: \(\frac{99}{9}=11\).

Step 2: Find Median

Arrange: \(5, 5, 10, 12, 12, 12, 13, 14, 16\). Middle number (5th) is \(12\).

Step 3: Determine Mode

\(12\) appears 3 times, most frequent.

Part e:

Step 1: Calculate Mean

Sum: \(15 + 18 + 19 + 20 + 22 + 24 + 22 = 140\). Divide by 7: \(\frac{140}{7}=20\).

Step 2: Find Median

Arrange: \(15, 18, 19, 20, 22, 22, 24\). Middle number (4th) is \(20\).

Step 3: Determine Mode

\(22\) appears 2 times, most frequent (tied? No, 22 twice, others once).

Part f:

Step 1: Calculate Mean

Sum: \(42 + 34 + 36 + 24 + 34 = 170\). Divide by 5: \(\frac{170}{5}=34\).

Step 2: Find Median

Arrange: \(24, 34, 34, 36, 42\). Middle number (3rd) is \(34\).

Step 3: Determine Mode

\(34\) appears 2 times, most frequent.

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