Answer to Question #336496 in Statistics and Probability for Tom

Question

5.6 Assessment Task

Directions. Answer the following items. You may use online calculators and solvers in answering.

1. For each of the following data sets determine the mean:

a. 72, 14,8, 11,57,54,31, 11,67,11,19,3,66 b. 63,9,87,16, 2, 96,13,67,34

c. 1,6,8,2,7,2,9,4,8,9,8,6 d. 12, 0,4,5,8, 3,6, 35,47

e. 2, 7, 17, 33, 67,73, 88, 33, 92, 57,33

2. For each of the following data sets determine the median:

a. 48, 78, 10, 66, 45, 57,96,67, 40, 66, 63,8, 20 b. 28, 3, 10, 60, 8, 23, 45, 97,11, 10

c. 6,9,1, 6, 4, 8, 1, 7, 8, 3, 1, 0

d. 63, 9, 86, 16, 2, 97,24, 67, 34,40 e. 8, 4, 64, 99, 11, 42, 15,88, 54, 77,42

3. For each of the following data sets determine the mode:

a. 98, 37,5,33, 96, 67, 43, 33, 91, 33,32,8,11 b. 104, 2, 51,31,8, 101, 104, 18,47

c. 3, 4, 5, 3,9,8,5,7,2,5,1

d. 19, 1,9,6,4,2,13,15,24,2

e. 8,9,39,44,55,90,19,44,28,69,44

43/76

Answer 1

1.

a.

$$mean=\dfrac{1}{13}(98+37+5+33+96+67$$

$$+43+33+91+33+32+8+11)=\dfrac{587}{13}$$

b.

$$mean=\dfrac{1}{9}(63+9+87+16+2+96+13$$

$$+67+34)=43$$

c.

$$mean=\dfrac{1}{12}(1+6+8+2+7+2+9$$

$$+4+8+9+8+6)=\dfrac{35}{6}$$

d.

$$mean=\dfrac{1}{9}(12+0+4+5+8+3+6+35+47)$$

$$=\dfrac{40}{3}$$

e.

$$mean=\dfrac{1}{11}(2+7+17+33+67+73$$

$$+88+33+92+57+33)=\dfrac{502}{11}$$

2.

a.

$$8,10,20,40,45,48, 57,63,66,66,67,78, 96$$

$$median=57$$

b.

$$3,8,10,10,11, 23, 28, 45, 60, 97$$

$$median=\dfrac{11+23}{2}=17$$

c.

$$0,1,1,1,3,4,6,6,7,8,8,9$$

$$median=\dfrac{4+6}{2}=5$$

d.

$$2,9,16, 24,34,40, 63, 67, 86, 97$$

$$median=\dfrac{34+40}{2}=37$$

e.

$$4,8, 11,15, 42, 42, 54, 64, 77, 88, 99$$

$$median=42$$

3.

a.

$$5,8,11,32, 33,33, 33, 37, 43, 67, 91, 96, 98$$

$$mode=33\ appeared\ 3\ times$$

b.

$$2,8, 18, 31,47, 51, 101, 104, 104$$

$$mode=104\ appeared\ 2\ times$$

c.

$$1, 2, 3, 3, 4, 5, 5, 5, 7, 8, 9$$

$$mode=5\ appeared\ 3\ times$$

d.

$$1,2,2,4, 6, 9, 13, 15,19, 24$$

$$mode=2\ appeared\ 2\ times$$

e.

$$8,9, 19, 28, 39,44, 44, 44, 55, 69, 90$$

$$mode=44\ appeared\ 3\ times$$