QUESTION IMAGE
Question
sonya randomly surveys 26 seventh graders to gather data about the most seventh graders use the internet a little more than 7 hours each click the icon to view the dot plot.
a. the mean of sonyas data is 7.5 hours. (type an integer or a dec
b. the median of sonyas data is \\(\square\\) hours. (type an integer or a dec
dot plot
weekly internet use
0 1 2 3 4 5 6 7 8 9 10 11
number of hours
)+5(10)=2+1=3+2=5+8=13+3=16+5=21+5=26. So:
3:2 (positions 1,2)
4:1 (position 3)
5:2 (positions 4,5)
7:8 (positions 6-13: 6,7,8,9,10,11,12,13)
8:3 (positions 14-16:14,15,16)
9:5 (positions 17-21:17,18,19,20,21)
10:5 (positions 22-26:22,23,24,25,26)
Now, to find the median, we need the middle value(s) since n=26 (even number). The median is the average of the 13th and 14th values.
Let's find the 13th and 14th values.
Positions 1-2: 3
3:4
4-5:5
6-13:7 (since 6 to 13 is 8 values: 6,7,8,9,10,11,12,13 → 8 values, so 6th to 13th are 7s)
Then 14th value: 8 (since 14th is the first of the 8s? Wait no, 13th is 7 (position 13), 14th is 8 (position 14). Wait:
Wait positions:
1:3
2:3
3:4
4:5
5:5
6:7
7:7
8:7
9:7
10:7
11:7
12:7
13:7
14:8
15:8
16:8
17:9
18:9
19:9
20:9
21:9
22:10
23:10
24:10
25:10
26:10
Ah, there we go. So 13th value is 7 (position 13), 14th value is 8 (position 14). Wait no, wait position 13: let's count again.
Wait 3:2 (1,2)
4:1 (3)
5:2 (4,5)
7:8 (6,7,8,9,10,11,12,13) → so position 6 to 13: 8 values, so position 13 is 7.
Then position 14: 8 (since 8 has 3 values: positions 14,15,16)
So the 13th value is 7, 14th is 8. Then median is (7 + 8)/2 = 7.5? Wait no, wait that can't be. Wait no, maybe my frequency count is wrong.
Wait maybe the dot plot at 7 has 6 dots, 8 has 3, 9 has 4, 10 has 4. Let's recalculate:
3:2, 4:1, 5:2, 7:6, 8:3, 9:4, 10:4. Then 2+1=3+2=5+6=11+3=14+4=18+4=22. No, still not 26.
Wait the problem says 26 seventh graders. So total data points:26.
Let's look at the dot plot again. The x-axis is 0-11, with dots at 3,4,5,7,8,9,10.
At 3: two dots.
At 4: one dot.
At 5: two dots.
At 7: let's count the number of dots: the vertical line at 7, how many? Let's say 7 dots (since it's the tallest, maybe 7).
At 8: three dots.
At 9: five dots.
At 10: five dots.
So 2+1+2+7+3+5+5=25. Missing 1. So maybe 7 has 8 dots. Then 2+1+2+8+3+5+5=26. Yes.
So positions:
1:3
2:3
3:4
4:5
5:5
6:7
7:7
8:7
9:7
10:7
11:7
12:7
13:7
14:8
15:8
16:8
17:9
18:9
19:9
20:9
21:9
22:10
23:10
24:10
25:10
26:10
So 13th value: position 13 is 7 (since 6-13 are 7s: 8 values, so 13 is 7).
14th value: position 14 is 8.
So median is (7 + 8)/2 = 7.5? Wait but the mean is 7.5. But maybe I made a mistake.
Wait no, maybe the dot plot at 7 has 7 dots, 8 has 3, 9 has 5, 10 has 5, and 6 has 1 dot? Wait the x-axis is 0-11, maybe 6 has 1 dot? Let's check:
3:2, 4:1, 5:2, 6:1, 7:7, 8:3, 9:5, 10:5. Then 2+1+2+1+7+3+5+5=26. Ah! That works. I missed 6. So 6 has 1 dot.
So now, let's list the frequencies:
3:2
4:1
5:2
6:1
7:7
8:3
9:5
10:5
Now total:2+1=3+2=5+1=6+7=13+3=16+5=21+5=26. Perfect.
Now, let's order the data:
3,3,4,5,5,6,7,7,7,7,7,7,7,8,8,8,9,9,9,9,9,10,10,10,10,10.
Now, let's list the positions:
1:3
2:3
3:4
4:5
5:5
6:6
7:7
8:7
9:7
10:7
11:7
12:7
13:7
14:8
15:8
16:8
17:9
18:9
19:9
20:9
21:9
22:10
23:10
24:10
25:10
26:10
Now, n=26, so median is the average of the 13th and 14th values.
13th value: position 13 is 7 (since position 13: let's count:
1:3, 2:3, 3:4, 4:5, 5:5, 6:6, 7:7, 8:7, 9:7, 10:7, 11:7, 12:7, 13:7.
14th value: position 14 is 8.
So median is (7 + 8)/2 = 7.5? Wait but the mean is 7.5. But maybe that's correct. Wait no, wait the 13th value is 7, 14th is 8, so (7+8)/2=7.5.
Wait but let's check again. The data points:
After 6 (position 6), we have seven 7s? Wait no, 7 has 7 dots: positions 7-13 (7 dots: 7,7,7,7,7,7,7). Then position 14:8.
Yes, so 13th is 7, 14th is 8. So median is (7+8)/2=7.5. Wait but the mean is also 7.5. Is that…
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