Question

typing speed (words per minute)
group 1\tgroup 2
9 7 5 4 3\t1 6 6 7 9
6 5 5 4 0\t4 0 2 5 7
9 9 7 5 4 0\t5 0 0 3 5 6 8 9
7\t6 4
(a) which group had more typing speeds in the 30s?
\t○ group 1
\t○ group 2
\t○ each had the same
(b) which group had the greater median typing speed?
\t○ group 1
\t○ group 2
\t○ the medians were the same
(c) what were the ranges of typing speeds for the two groups?
group 1
words per minute
group 2
words per minute

Explanation:

Part (a)

Step1: Analyze Group 1's 30s speeds

Group 1 data (typing speeds, stem - leaf plot: stem is tens place, leaf is ones place). For 30s (stem = 3), Group 1 has leaf 1,6,6,7,9? Wait, no, looking at the stem - leaf:

Group 1:

• Stem 3: leaves 1,6,6,7,9? Wait, no, the stem - leaf for Group 1:

Wait the table:

Group 1:
Stem 3: 1,6,6,7,9? Wait no, the original data:

Wait the stem - leaf is presented as:

Group 1:
9 7 5 4 (wait no, the yellow box:

Group 1:
9 7 5 4
6 5 5 4 0
9 9 7 5 4 0
7

Wait maybe it's a stem - leaf plot where stem is the tens digit. Let's re - interpret:

For Group 1:

• Stem 3: Wait no, maybe the first column is Group 1, second Group 2. Wait the x - axis (stem) is 3,4,5,6,7? Wait the stem is the tens place, leaves are ones.

Wait Group 1:

• Stem 3: leaves 1,6,6,7,9? No, looking at the numbers:

Wait the user's image:

Group 1:
Row 1: 9 7 5 4 (maybe stem 3? No, maybe the stem is 3,4,5,6,7. Let's list Group 1's data:

Group 1 typing speeds (words per minute):

• For stem 3: 31, 36, 36, 37, 39?
• Stem 4: 40,42,45,47? Wait no, the leaves for Group 1:

Wait the yellow box:

Group 1:
9 7 5 4 (maybe stem 3: 34, 35, 37, 39? Wait no, maybe the stem is the first digit, leaf is the second. Wait maybe the data is:

Group 1: 39, 37, 35, 34, 46, 45, 45, 44, 40, 59, 59, 57, 55, 54, 50, 67? Wait no, this is confusing. Wait maybe a better way: count the number of data points in the 30s (i.e., 30 - 39) for each group.

Group 1: Let's find how many values are between 30 - 39.

Looking at Group 1's data (from the stem - leaf, assuming stem is tens place):

Group 1:

• Stem 3: leaves (let's say the first row under Group 1 is stem 3: 34, 35, 37, 39? Wait no, the first line of Group 1: 9 7 5 4 – maybe it's 39, 37, 35, 34 (since 30 + 9 = 39, 30+7 = 37, 30 + 5 = 35, 30+4 = 34). Then second line: 6 5 5 4 0 – 46, 45, 45, 44, 40 (40 + 6? No, 40 + 6 = 46? Wait no, tens digit is 4: 46, 45, 45, 44, 40. Third line: 9 9 7 5 4 0 – 59, 59, 57, 55, 54, 50 (tens digit 5). Fourth line: 7 – 67 (tens digit 6? No, 67? Wait no, 70 + 7 = 77? No, this is getting too confusing. Wait maybe the key is that Group 2 has more data in the 30s? Wait no, let's look at Group 2:

Group 2:
Stem 3: leaves 1,6,6,7,9 (so 31, 36, 36, 37, 39) – that's 5 values in 30s.

Group 1: Let's see, if Group 1's stem 3 data is, say, 34, 35, 37, 39 (4 values). So Group 2 has more in the 30s? Wait no, the question (a) is "Which group had more typing speeds in the 30s?".

Wait maybe I mis - interpreted. Let's assume:

Group 1's data in 30s (30 - 39): Let's count the number of data points for Group 1 between 30 - 39.

Looking at the stem - leaf, Group 1:

• Numbers in 30 - 39: Let's list all Group 1 numbers:

From the image:

Group 1: 34, 35, 37, 39, 40, 44, 45, 45, 46, 50, 54, 55, 57, 59, 59, 67? Wait no, maybe the data is:

Group 1: 34, 35, 37, 39, 40, 44, 45, 45, 46, 50, 54, 55, 57, 59, 59, 67 (wait that's 16 numbers? No, maybe the stem - leaf is:

Stem (tens) | Group 1 (leaves) | Group 2 (leaves)
--- | --- | ---
3 | 4,5,7,9 | 1,6,6,7,9
4 | 0,4,5,5,6 | 0,2,5,7
5 | 0,4,5,7,9,9 | 0,0,3,5,6,8,9
6 | 7 | 4
7 | |

So for stem 3 (30 - 39):

Group 1: 34, 35, 37, 39 (4 values)
Group 2: 31, 36, 36, 37, 39 (5 values)

So Group 2 has more in the 30s? Wait no, the options are Group 1, Group 2, Each had the same. Wait maybe I got Group 1 and Group 2 reversed.

Wait the stem - leaf:

First column: Group 1, second: Group 2.

Stem 3:

Group 1 leaves: 4,5,7,9 → 34, 35, 37, 39

Group 2 leaves: 1,6,6,7,9 → 31, 36, 36, 37, 39

Stem 4:

Group 1 leaves: 0,4,5,5,6 → 40, 44, 45, 45, 46

Group 2 leaves: 0,2,5,7 → 40,…

To find the median, we first order the data.

For Group 1:

First, list all data points (from stem - leaf, now assuming Group 1 is the right column):

Group 1 data:

Stem 3: 31, 36, 36, 37, 39

Stem 4: 40, 42, 45, 47

Stem 5: 50, 50, 53, 55, 56, 58, 59

Stem 6: 64

Wait no, wait the stem - leaf:

Wait let's correctly list Group 1 (right column) and Group 2 (left column):

Group 1 (right column) data:

• Stem 3: 31, 36, 36, 37, 39 (5 values)
• Stem 4: 40, 42, 45, 47 (4 values)
• Stem 5: 50, 50, 53, 55, 56, 58, 59 (7 values)
• Stem 6: 64 (1 value)

Total data points for Group 1: 5 + 4+7 + 1=17. The median is the 9th value (since (17 + 1)/2 = 9th term).

Ordering Group 1 data:

31, 36, 36, 37, 39, 40, 42, 45, 47, 50, 50, 53, 55, 56, 58, 59, 64

9th term: 47

Group 2 (left column) data:

• Stem 3: 34, 35, 37, 39 (4 values)
• Stem 4: 40, 44, 45, 45, 46 (5 values)
• Stem 5: 50, 54, 55, 57, 59, 59 (6 values)
• Stem 6: 67 (1 value)

Total data points for Group 2: 4+5 + 6+1 = 16. The median is the average of the 8th and 9th terms.

Ordering Group 2 data:

34, 35, 37, 39, 40, 44, 45, 45, 46, 50, 54, 55, 57, 59, 59, 67

8th term: 45, 9th term: 46. Median = (45 + 46)/2 = 45.5

Now, Group 1 median is 47, Group 2 median is 45.5. So Group 1 has a greater median.

Part (c)

The range of a data set is calculated as \( \text{Range}=\text{Maximum value}-\text{Minimum value} \)

For Group 1:

Minimum value: 31, Maximum value: 64. Range = 64 - 31 = 33

For Group 2:

Minimum value: 34, Maximum value: 67. Range = 67 - 34 = 33

Wait no, wait Group 1 data:

Wait Group 1 (right column) maximum is 64, minimum is 31. Range = 64 - 31 = 33

Group 2 (left column) maximum is 67, minimum is 34. Range = 67 - 34 = 33? Wait no, 67 - 34 = 33? 67 - 34 = 33? Yes, 34+33 = 67.

Wait let's re - check:

Group 1: min = 31, max = 64. 64 - 31 = 33

Group 2: min = 34, max = 67. 67 - 34 = 33

Wait that's correct.

Answer:

s:

(a) Group 1

(b) Group 1

(c) Group 1: 33 words per minute, Group 2: 33 words per minute (Wait no, wait Group 2's max is 67, min is 34. 67 - 34 = 33. Group 1's max is 64, min is 31. 64 - 31 = 33. So both have a range of 33.