Estimating Mean Running Time and Interquartile Range of Family Movies

The running time t of 200 family movies are recorded in the following table. Write down the mid interval value of t

greater than or equal to 70 less than 80. Mid interval value equals 70 + 80 over

2. So we get 75. Calculate an estimate of the mean running

time of the 200 movies. First of all, we need to figure out mid interval value.

75 80 + 85 over 2 82.5 87.5

92.5 100 Then we need to put this into calculator to figure out the mean. Since

uh this is a frequency so only have one variable we need to go to one variable stats click

on one then no we will go to four name column one as a

P then column B as the frequency. So, FR. After you put in all the

values, click on an empty cell menu for statistics, one stats

calculations. This is a one variable stats because the second column is a

frequency. For one variable stats, number of leads is always one. Then enter. Right arrow button to get t as x1

list. for frequency list it's

a fr then enter so we get this xbar which is mean

is 88.15 since this is two marks so we need to show the work xbar equals

75 * 11 82.5 * 51 87.5

* 68 92.5 *

47 100 * 23 all over frequency add all these together equals 200

100 equals 88.15. This table is used to create the

following cumulative frequency graph. Use the cumulative frequency curve to estimate

the inter quartile range. Intercortile range IQR equals Q3 minus Q1.

Q3 it's 75%. So 75%

times cumulative frequency total is 200 equals

150. Get 150. Then going down. Then you need to

check the unit for running time from 70 to 75.

We count how many small units here. 75 minus 70 over 10 equals

0.5. So 90 plus we have three units of

0.5. 90 + 3 * 0.5 is 91.5. For Q1, the first quartile equals 25%. So

25% times the total number 200 equals

50. So get this 50. Draw this horizontal line. Then going

down 80 plus all together is a eight each is a

0.5. So we get 84 equals 91.5 minus

84 equals 7.5. Starfield is a movie in the data set and its running time is 100 minutes. Use

your answer to part B to estimate whether Starfield's running time is an outlier for this data. Justify your

answer. We have a lower outlier. We will use the

closest quartile minus

1.5 IQR higher

outlier closest quartile is Q3 add 1.5

IQR we will find the higher outline liar equals Q3 is

91.5 + 1.5 * 7.5 = 102.75.

Since 100 less than 102.75, it's a not an outlier.