Question

1. Forty randomly selected students were asked the number of pairs of sneakers they owned. Let X = the number of pairs of sneakers owned. The results are as follows.

X	Frequency
1	2
2	5
3	6
4	13
5	13
6	1

A. Find the sample standard deviation, s. (Round your answer to two decimal places.) answer is NOT 1.22

B. Complete the columns of the chart. (Round your answers to three decimal places.) Fill in chart for relative frequency and cumulative relative frequency.

X	Frequency	Relative Frequency	Cumulative Relative Frequency
1	2
2	5
3	6
4	13
5	13
6	1

C. Find the first quartile. Answer is NOT 2.0

D. Find the median. Answer is NOT 5.5

E. Find the third quartile. Answer is NOT 5.5

_______________________________________________________________________________________________________________________________________2. A music school has budgeted to purchase 3 musical instruments. They plan to purchase a piano costing $3,000, a guitar costing $550, and a drum set costing $650. The mean cost for a piano is $3,500 with a standard deviation of $2,500. The mean cost for a guitar is $450 with a standard deviation of $250. The mean cost for drums is $750with a standard deviation of $100. (Enter your answers to two decimal places.)

A. How many standard deviations above or below the average piano cost is the piano?

______ standard deviations below the average

B. How many standard deviations above or below the average drum set cost is the drum set?

______ standard deviations below the average

C. Which cost is the lowest, when compared to other instruments of the same type? (Choose one.)

- drum set

- piano

- guitar

D. Which cost is the highest when compared to other instruments of the same type. (Choose one.)

- drum set

- piano

- guitar

Answer 1

Answer 1A)

Thus, standard deviation is 1.24 (Rounded to 2 decimal places)

Answer 1B)

X	Frequency (f)	Relative Frequency	Cumulative Relative Frequency
1	2	2/40 = 0.050	0.050
2	5	5/40 = 0.125	0.050+0.125 = 0.175
3	6	6/40 = 0.150	0.175+0.150 = 0.325
4	13	13/40 = 0.325	0.325+0.325 = 0.650
5	13	13/40 = 0.325	0.650+0.325 = 0.975
6	1	1/40 = 0.025	0.975+0.025 = 1.000

Answer 1C)

X	Frequency (f)	Cumulative Frequency
1	2	2
2	5	2+5= 7
3	6	7+6 = 13
4	13	13+13 = 26
5	13	26+13 = 39
6	1	39+1 = 40

For Q1​ we have to compute the following position:

pos(Q1​) = (n+1)*(25/100) ​= (40+1)*(25/100) ​= 10.25

Since 10.25 is not an integer number, Q1​ is computed by interpolating between the values located in 10th and 11th positions, as shown in the formula below

Based on cumulative frequency table, we can see that number on 10th and 11th positions is 3.

So, Q1​ = 3 + (10.25-10)×(3-3)

First quartile Q1​ = 3

Answer 1D)

Since the sample size n = 40 is even, we have that (n+1)/2 = (40+1)/2 = 20.5 is not an integer value, the median is computing by taking the average of the values at the positions 20th and 21th, as shown below

Based on cumulative frequency table, we can see that number on positions 20th and 21th is 4.

So, Median = (4+4)/2

Median = 4

Answer 1E)

For Q3​ we have to compute the following position:

pos(Q3​)=(n+1)*(75/100) ​= (40+1)*(75/100) =30.75

Since 30.75 is not an integer number, Q3​ is computed by interpolating between the values located in the 30th and 31th positions, as shown in the formula below

Based on cumulative frequency table, we can see that number on 30th and 31th positions is 4.

Q3​ = 5+(30.75−30)×(5−5)

Third quartile Q3​ = 5

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