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:

Part a:

Step1: Calculate Mean

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

Step2: Calculate Median

Sort the numbers: \(3, 4, 4, 5, 9\). Middle term (3rd) is \(4\), so \(\text{Median} = 4\).

Step3: Calculate Mode

The number \(4\) appears most (twice), so \(\text{Mode} = 4\).

Part b:

Step1: Calculate Mean

Sum: \(8 + 4 + 5 + 8 + 5 + 4 + 8 = 42\). \(n = 7\), so \(\text{Mean} = \frac{42}{7}=6\).

Step2: Calculate Median

Sort: \(4, 4, 5, 5, 8, 8, 8\). Middle term (4th) is \(5\), so \(\text{Median} = 5\).

Step3: Calculate Mode

\(8\) appears most (thrice), so \(\text{Mode} = 8\).

Part c:

Step1: Calculate Mean

Sum: \(10 + 13 + 11 + 13 + 13 = 50\). \(n = 5\), so \(\text{Mean} = \frac{50}{5}=12\).

Step2: Calculate Median

Sort: \(10, 11, 13, 13, 13\). Middle term (3rd) is \(13\), so \(\text{Median} = 13\).

Step3: Calculate Mode

\(13\) appears most (thrice), so \(\text{Mode} = 13\).

Part d:

Step1: Calculate Mean

Sum: \(5 + 12 + 13 + 16 + 12 + 14 + 12 + 5 + 10 = 99\). \(n = 9\), so \(\text{Mean} = \frac{99}{9}=11\).

Step2: Calculate Median

Sort: \(5, 5, 10, 12, 12, 12, 13, 14, 16\). Middle term (5th) is \(12\), so \(\text{Median} = 12\).

Step3: Calculate Mode

\(12\) appears most (thrice), so \(\text{Mode} = 12\).

Part e:

Step1: Calculate Mean

Sum: \(15 + 18 + 19 + 20 + 22 + 24 + 22 = 140\). \(n = 7\), so \(\text{Mean} = \frac{140}{7}=20\).

Step2: Calculate Median

Sort: \(15, 18, 19, 20, 22, 22, 24\). Middle term (4th) is \(20\), so \(\text{Median} = 20\).

Step3: Calculate Mode

\(22\) appears most (twice), so \(\text{Mode} = 22\).

Part f:

Step1: Calculate Mean

Sum: \(42 + 34 + 36 + 24 + 34 = 170\). \(n = 5\), so \(\text{Mean} = \frac{170}{5}=34\).

Step2: Calculate Median

Sort: \(24, 34, 34, 36, 42\). Middle term (3rd) is \(34\), so \(\text{Median} = 34\).

Step3: Calculate Mode

\(34\) appears most (twice), so \(\text{Mode} = 34\).

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. \(42, 34, 36, 24, 34\)	\(34\)	\(34\)	\(34\)