Question

probability and statistics
1.3 displaying quantitative data:
dotplots graded classwork
name:
date:
period: 1
read each set of directions very carefully. answer each completely.
1.)

here are data on the lengths of the first 25 words on a randomly selected page from harry potter and the prisoner of azkaban.
2, 3, 4, 10, 2, 11, 2, 8, 4, 3, 7, 2, 7, 5, 3, 6, 4, 4, 2, 5, 8, 2, 3, 4, 4

(a) which of the following is the correct dotplot of these data?

(b) explain what the dot above 6 represents.
the dot above 6 represents the, __ (6 characters) of __ of the first 25 words on a randomly selected page from harry potter and the prisoner of azkaban.

(c) what percent of the words have more than 4 letters? box with 36% % (enter an integer)

Explanation:

Part (a)

To determine the correct dotplot, we first count the frequency of each word length:

• Length 2: Let's count how many times 2 appears. The data is 2, 3, 4, 10, 2, 11, 2, 8, 4, 3, 7, 2, 7, 5, 3, 6, 4, 4, 2, 5, 8, 2, 3, 4, 4. Counting 2s: positions 1,5,7,12,19,22. So 6 times.
• Length 3: Positions 2,10,15,23. Wait, let's list all: 3 (pos2), 3 (pos10), 3 (pos15), 3 (pos23). Wait, no, let's recount: 3 appears at 2,10,15,23? Wait the data is: 2, 3, 4, 10, 2, 11, 2, 8, 4, 3, 7, 2, 7, 5, 3, 6, 4, 4, 2, 5, 8, 2, 3, 4, 4. So 3s: pos2,10,15,23? Wait no, pos2:3, pos10:3, pos15:3, pos23:3? Wait that's 4? Wait no, let's count again: 3,3,3,3? Wait no, the data has 3 at positions 2,10,15,23? Wait no, let's list all numbers:

Data list: 2, 3, 4, 10, 2, 11, 2, 8, 4, 3, 7, 2, 7, 5, 3, 6, 4, 4, 2, 5, 8, 2, 3, 4, 4.

Count of 2: Let's mark each 2: index 0 (2), 4 (2), 6 (2), 11 (2), 18 (2), 21 (2). So 6 times.

Count of 3: index 1 (3), 9 (3), 14 (3), 22 (3). So 4 times.

Count of 4: index 2 (4), 8 (4), 16 (4), 17 (4), 23 (4), 24 (4). Wait index 2:4, 8:4, 16:4, 17:4, 23:4, 24:4? Wait no, the data has 4 at positions 2,8,16,17,23,24? Wait let's count: 4 appears 6 times? Wait the data is 25 numbers. Let's count total:

2:6, 3:4, 4: let's see: 4 (pos2), 4 (pos8), 4 (pos16), 4 (pos17), 4 (pos23), 4 (pos24). Wait that's 6? Wait no, 2 (6) + 3 (4) +4 (let's count again: 4,4,4,4,4,4? Wait the data is: 2,3,4,10,2,11,2,8,4,3,7,2,7,5,3,6,4,4,2,5,8,2,3,4,4. So 4s: pos2,8,16,17,23,24. That's 6. Then 5: pos13,19. So 2 times. 6: pos15. 1 time. 7: pos10? No, pos10 is 3, pos11 is 7, pos12 is 7. So 7:2 times. 8: pos7,20. 2 times. 10: pos3. 1 time. 11: pos5. 1 time.

Now, the first dotplot (the one with the most dots at 2, then 3, then 4, etc.) should match these frequencies. So the correct dotplot is the first one (the one with the shaded option, likely the top-left) because it has 6 dots at 2, 4 at 3, 6 at 4, 2 at 5, 1 at 6, 2 at 7, 2 at 8, 1 at 10, 1 at 11.

Part (b)

The dot above 6 in the dotplot represents the number of words with length 6. From the data, we saw that the length 6 appears once. So the dot above 6 represents that there is 1 word with 6 characters (length 6) among the first 25 words on the randomly selected page.

Part (c)

Step1: Count words with >4 letters

First, identify the word lengths greater than 4: 5,6,7,8,10,11.

Count the frequency of each:

• Length 5: 2 (from data: 5,5)
• Length 6: 1 (6)
• Length 7: 2 (7,7)
• Length 8: 2 (8,8)
• Length 10: 1 (10)
• Length 11: 1 (11)

Total words with >4 letters: \(2 + 1 + 2 + 2 + 1 + 1 = 9\)

Step2: Calculate percentage

Total words: 25.

Percentage = \(\frac{\text{Number of words with >4 letters}}{\text{Total words}} \times 100 = \frac{9}{25} \times 100 = 36\)

Answer:

(a) The correct dotplot is the first one (the shaded/top - left option).
(b) The dot above 6 represents that there is 1 word with 6 characters (length 6) among the first 25 words.
(c) \(\boxed{36}\)