Question

Question 12 (1 point) The scores of a bowler for his last 29 games are ordered and shown below: 139 142 144 149 156 176 177 178 179 179 181 182 183 185 185 189 190 190 190 191 197 199 201 203 207 212 220 227 228 What is the first quartile of scores for this sample of games? Your Answer: Answer Question 13 (1 point) The ages of guests checking into a flight are summarized in the following frequency distribution: Age Frequency 0-10 4 10-20 5 20-30 4 30-40 6 40-50 20 50-60 32 60-70 22 70-80 1 Which interval contains the third quartle of data values?

Answer 1

We will use Tukey's method of finding the quartiles.

Q 12) First we need to find the position of the median for these 29 observations. When n is odd the median observation is (n+1)/2th observation, of an ordered sample.

Hence here the median observation is (29+1)/2=15

the 15th observation is the median.

Now the first Quartile is the median of the first 15 observations. Since there are odd number of observations (15), the median is (15+1)/2=8th observation.

The first quartile is the 8th observation

ans: The first quartile of scores for this sample of games is 178

Q 13) First we find the total number of sample in the table using the sum of frequencies

$n=4+ 5+ 4+ 6+ 20+ 32+ 22+ 1=94$

Since the number of observations is even the median is the average of n/2 th and n/2+1 th observations.

That is the median is the average of 94/2=47th and 48th observations.

Using the cumulative frequency table

Age	Frequency	Cumulative Frequency
0-10	4	4
10-20	5	9
20-30	4	13
30-40	6	19
40-50	20	39
50-60	32	71
60-70	22	93
70-80	1	94

we can see that the 47th and 48th observations are in the class 50-60.

The third quartile is the median of the observations which are more than the median

The observations which are more than the median are 48th to 94th observations.

That means there are 47 observations between 48th and 94th (including the 48th and 94th)

The median of these 47 observations is (47+1)/2=24th observation. That is the 24th observation starting from 48th is the median and hence the third quartile.

That means the third quartile is the 48+24-1=71st observation

Using the cumulative frequency above, we can see that the 71st observation is in the class 50-60

ans: The third quartile of data values is in the interval 50-60