125. the stemplot shows the number of home runs hit by each of the 30 major league baseball teams in a single season. home run totals above what value should be considered outliers?
09 | 15
10 | 3789
11 | 47
12 | 19
13 |
14 | 89
15 | 34445
16 | 239
17 | 235
18 | 326
19 | 1
20 | 3
21 | 0
22 | 2
key: 14|8 is a team with 148 home runs.
(a) 173 (b) 210 (c) 222 (d) 229 (e) 257
126. which of the following boxplots best matches the distribution shown in the histogram?
(a) data
(b) data
(c) data
(d) data
(e) data

Question

125. the stemplot shows the number of home runs hit by each of the 30 major league baseball teams in a single season. home run totals above what value should be considered outliers?
09 | 15
10 | 3789
11 | 47
12 | 19
13 |
14 | 89
15 | 34445
16 | 239
17 | 235
18 | 326
19 | 1
20 | 3
21 | 0
22 | 2
key: 14|8 is a team with 148 home runs.
(a) 173  (b) 210  (c) 222  (d) 229  (e) 257
126. which of the following boxplots best matches the distribution shown in the histogram?
(a) data
(b) data
(c) data
(d) data
(e) data

Accepted Answer

### Question 125
# Explanation:
## Step 1: Recall the outlier formula
To find outliers, we use the interquartile range (IQR) method. The formula for outliers is: values above $ Q_3 + 1.5 \times \text{IQR} $ or below $ Q_1 - 1.5 \times \text{IQR} $ are outliers. First, we need to find $ Q_1 $, $ Q_3 $, and IQR from the stemplot.

## Step 2: Organize the data from the stemplot
The stemplot data (home runs) for 30 teams:
- 09: 0,9 (wait, no, key is 14|8 is 148, so stems are tens place, leaves are ones. Wait, let's correct:
Stem 09: 09? Wait, no, stem 10: 3,7,8,9 (so 103, 107, 108, 109)
Stem 11: 4,7 (114, 117)
Stem 12: 1,9 (121, 129)
Stem 13: (no leaves? Wait, original stemplot:
09: 15? Wait, maybe I misread. Let's re-express the stemplot correctly with key 14|8 = 148. So stem is tens (and maybe hundreds? Wait, 14|8 is 148, so stem is 14 (tens and hundreds? Wait, 148: 1 (hundreds), 4 (tens), 8 (ones). Wait, maybe stem is the first two digits? Wait, 09: 15? No, maybe the stemplot is:

Stem 09: 1,5? No, the key is 14|8 is 148, so stem is 14 (i.e., 140s), leaf 8 is 8, so 148. So let's list all data points:

Stem 09: Wait, maybe the stem is the tens digit? No, 14|8 is 148, so stem is 14 (two digits), leaf is 8. So:

Stem 09: 1,5? Wait, the stemplot as given:

09 | 15

10 | 3789

11 | 47

12 | 19

13 | (empty)

14 | 89

15 | 34445

16 | 239

17 | 235

18 | 326

19 | 1

20 | 3

21 | 0

22 | 2

Wait, maybe the stem is the tens digit, and for stem 09, it's 9 (tens) with leaves 1,5? No, key is 14|8 is 148, so stem is 14 (i.e., 140-149), leaf 8 is 8, so 148. So:

Stem 09: 9 (tens) with leaves 1,5? No, 09 would be 9 (tens) but 09 is 90s? Wait, maybe the stem is the number of tens, so stem 9: 90s, stem 10: 100s, etc. But key is 14|8 is 148, so stem 14: 140s, leaf 8: 8, so 148. So let's list all data:

Stem 09: 91, 95 (wait, 09|15: 91, 95)

Stem 10: 103, 107, 108, 109

Stem 11: 114, 117

Stem 12: 121, 129

Stem 13: (no data)

Stem 14: 148, 149

Stem 15: 153, 154, 154, 154, 155

Stem 16: 162, 163, 169

Stem 17: 172, 173, 175

Stem 18: 183, 182, 186 (wait, 18|326: 183, 182, 186? Wait, leaf order? Maybe 18|3 2 6: 183, 182, 186? Or 18|326: 183, 182, 186? Wait, maybe leaves are in order, so 18|3 2 6: 183, 182, 186 (but usually leaves are in ascending order, so maybe 18|2 3 6: 182, 183, 186). Let's assume leaves are in ascending order.

Stem 19: 191

Stem 20: 203

Stem 21: 210

Stem 22: 222

Now, we have 30 data points. Let's list them in order:

91, 95,

103, 107, 108, 109,

114, 117,

121, 129,

148, 149,

153, 154, 154, 154, 155,

162, 163, 169,

172, 173, 175,

182, 183, 186,

191,

203,

210,

222

Wait, let's count:

Stem 09: 2

Stem 10: 4 (total 6)

Stem 11: 2 (8)

Stem 12: 2 (10)

Stem 13: 0 (10)

Stem 14: 2 (12)

Stem 15: 5 (17)

Stem 16: 3 (20)

Stem 17: 3 (23)

Stem 18: 3 (26)

Stem 19: 1 (27)

Stem 20: 1 (28)

Stem 21: 1 (29)

Stem 22: 1 (30). Yes, 30 data points.

Now, find $ Q_1 $ (25th percentile), $ Q_2 $ (median, 50th percentile), $ Q_3 $ (75th percentile).

For 30 data points, the median (Q2) is the average of the 15th and 16th terms.

Let's list the ordered data with indices (1 to 30):

1: 91

2: 95

3: 103

4: 107

5: 108

6: 109

7: 114

8: 117

9: 121

10: 129

11: 148

12: 149

13: 153

14: 154

15: 154

16: 154

17: 155

18: 162

19: 163

20: 169

21: 172

22: 173

23: 175

24: 182

25: 183

26: 186

27: 191

28: 203

29: 210

30: 222

Median (Q2): (15th + 16th)/2 = (154 + 154)/2 = 154.

Q1: 25th percentile, which is the median of the first 15 data points (indices 1-15).

First 15 data points:

1:91, 2:95, 3:103, 4:107, 5:108, 6:109, 7:114, 8:117, 9:121, 10:129, 11:148, 12:149, 13:153, 14:154, 15:154

Median of these 15 (8th term, since (15+1)/2=8): 8th term is 117. So Q1 = 117.

Q3: 75th percentile, median of the last 15 data points (indices 16-30).

Last 15 data points:

16:154, 17:155, 18:162, 19:163, 20:169, 21:172, 22:173, 23:175, 24:182, 25:183, 26:186, 27:191, 28:203, 29:210, 30:222

Median of these 15 (8th term, (15+1)/2=8): 8th term is 175. So Q3 = 175.

IQR = Q3 - Q1 = 175 - 117 = 58.

Now, upper outlier boundary: Q3 + 1.5*IQR = 175 + 1.5*58 = 175 + 87 = 262? Wait, that can't be, since the maximum is 222. Wait, maybe I made a mistake in data ordering.

Wait, maybe the stem 09 is 9 (tens) with leaves 1 and 5, so 91 and 95. Then stem 10: 103,107,108,109 (correct). Stem 11:114,117 (correct). Stem 12:121,129 (correct). Stem 13: empty. Stem 14:148,149 (correct). Stem 15:153,154,154,154,155 (correct). Stem 16:162,163,169 (correct). Stem 17:172,173,175 (correct). Stem 18:183,182,186? Wait, maybe the leaves are 3,2,6, but in ascending order, it's 2,3,6, so 182,183,186 (correct, indices 24,25,26). Stem 19:191 (27), stem 20:203 (28), stem 21:210 (29), stem 22:222 (30). So data is correct.

Wait, maybe the stem 09 is 09 (i.e., 9) with leaves 1 and 5, so 91 and 95. Then the first 15 data points:

1:91, 2:95, 3:103, 4:107, 5:108, 6:109, 7:114, 8:117, 9:121, 10:129, 11:148, 12:149, 13:153, 14:154, 15:154. So Q1 is the 8th term: 117. Correct.

Q3: last 15 data points (indices 16-30):

16:154, 17:155, 18:162, 19:163, 20:169, 21:172, 22:173, 23:175, 24:182, 25:183, 26:186, 27:191, 28:203, 29:210, 30:222. So 8th term is 175. Correct.

IQR = 175 - 117 = 58. Then upper outlier: 175 + 1.5*58 = 175 + 87 = 262. But the options are 173,210,222,229,257. None is 262. So I must have misinterpreted the stemplot.

Wait, maybe the stem is the tens digit, and for stem 09, it's 9 (tens) with leaves 1 and 5, but maybe the stem is 0 (tens) with leaves 9,1,5? No, key is 14|8=148, so stem is 14 (two digits), leaf 8. So stem 09: 09 (i.e., 9) with leaves 1 and 5: 91,95. Stem 10:10 with leaves 3,7,8,9:103,107,108,109. Stem 11:11 with leaves 4,7:114,117. Stem 12:12 with leaves 1,9:121,129. Stem 13:13 with no leaves. Stem 14:14 with leaves 8,9:148,149. Stem 15:15 with leaves 3,4,4,4,5:153,154,154,154,155. Stem 16:16 with leaves 2,3,9:162,163,169. Stem 17:17 with leaves 2,3,5:172,173,175. Stem 18:18 with leaves 3,2,6:183,182,186 (but sorted:182,183,186). Stem 19:19 with leaf 1:191. Stem 20:20 with leaf 3:203. Stem 21:21 with leaf 0:210. Stem 22:22 with leaf 2:222.

Wait, maybe the stem is the number of home runs in tens, so stem 9: 90-99, stem 10:100-109, etc. Then the data is:

91,95,

103,107,108,109,

114,117,

121,129,

148,149,

153,154,154,154,155,

162,163,169,

172,173,175,

182,183,186,

191,

203,

210,

222.

Now, let's recalculate Q1, Q2, Q3.

n=30, so:

Q1 is at position (30+1)*0.25 = 7.75, so 7th + 0.75*(8th -7th)

7th term:114, 8th term:117. So Q1 = 114 + 0.75*(117-114) = 114 + 2.25 = 116.25 ≈116 (but maybe using integer positions, since 30 is even, Q1 is median of first 15, which is (7th +8th)/2? Wait, no, for n=30, the first quartile is the median of the first 15 data points (positions 1-15). The first 15 data points:

1:91,2:95,3:103,4:107,5:108,6:109,7:114,8:117,9:121,10:129,11:148,12:149,13:153,14:154,15:1

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 125

Step 1: Recall the outlier formula

Step 2: Organize the data from the stemplot

Answer:

Step 1: Recall the outlier formula

Step 2: Organize the data from the stemplot