Question

Procedure

Search online for 30 movie titles. Record their length in min in the table below.

88 LK	115 Inc	161 HP2	130RGR	126 IM	125 Trn
83 LM	88 M	121 SM	121GG	124 IM2	133 RG1
103 D	100 FN	136AS	136 GG2	130 IM3	140 RVS
90 S	97 FD	131HC	149 IFN	134 BP	96 UP
92 MI	152 HP1	114 GR	162 AV	112 HLK	148 ADGH

Analyze the Distribution

Using your sample mean, sample standard deviation, and histogram to help, what was the approximate theoretical distribution of the data from the section titled "Collect the Data"?

X ~ How does the histogram help you arrive at the approximate distribution?

Describe the Data

Using the data in the section titled "Collect the Data" complete the following statements. (Hint: order the data)

REMEMBER: (IQR = Q3 - Q1)

_ IQR =

_ 15th percentile is:

_ 85th percentile is:

_ Median is:

_ What is the empirical probability that a randomly chosen movie length is more than 238 min?

_ Explain the meaning the 85th percentile of this data.

Answer 1

Analyze the Distribution

Using your sample mean, sample standard deviation, and histogram to help, what was the approximate theoretical distribution of the data from the section titled "Collect the Data"?

Sorted data

	Time
1	83
2	88
3	88
4	90
5	92
6	96
7	97
8	100
9	103
10	112
11	114
12	115
13	121
14	121
15	124
16	125
17	126
18	130
19	130
20	131
21	133
22	134
23	136
24	136
25	140
26	148
27	149
28	152
29	161
30	162

X ~ How does the histogram help you arrive at the approximate distribution?

Frequency Distribution - Quantitative
		Time
	lower		upper	midpoint	width	frequency	percent
	80	<	90	85	10	3	10.0
	90	<	100	95	10	4	13.3
	100	<	110	105	10	2	6.7
	110	<	120	115	10	3	10.0
	120	<	130	125	10	5	16.7
	130	<	140	135	10	7	23.3
	140	<	150	145	10	3	10.0
	150	<	160	155	10	1	3.3
	160	<	170	165	10	2	6.7
						30	100.0

The distribution looks like a bimodal distribution.

Describe the Data

Using the data in the section titled "Collect the Data" complete the following statements. (Hint: order the data)

30*75/100 =22.5

Q3 is 22.5^th observation in the ordered data ( average of 22 and 23 observation in the ordered data)

=(134+136)/2 = 135 min

30*25/100 =7.5

Q1 is 7.5^th observation in the ordered data

=( 97+100)/2 = 98.5 min

REMEMBER: (IQR = Q3 - Q1)

_ IQR =135-98.5 =36.5 min

_ 15th percentile is:

=4.5^th observation in the ordered data =(90+92)/2 =91 min

_ 85th percentile is:

=25.5^th observation in the ordered data =(140+148)/2 =144 min

_ Median is:

=middle observation in the ordered data =(124+125)/2 =124.5 min

_ What is the empirical probability that a randomly chosen movie length is more than 238 min?

Largest value in the data is 162 min

Therefore P( x > 238) =0.0

_ Explain the meaning the 85th percentile of this data.

85th percentile =144 min.

85% of the movie lengths are below 144 min.