The given stem and leaf plot shows the typing speeds of two groups of students.
Group 1 has n1= 20 students
Group 2 has n2= 19 students
The stem and leaf plot is two sided, meaning that they share the same stem.
The observed values are the number of words per minute.
In the steam the ten of each value is placed and in the leafs you find the units:
This way you can determine the observations for both samples. I'll do so and arrange them form least to greatest:
Group 1:
33, 34, 37, 42, 44, 44, 45, 47, 48, 49, 49, 50, 51, 52, 52, 55, 55, 63, 66, 67
Group 2:
33, 36, 41, 42, 44, 46, 46, 51, 52, 52, 52, 53, 53, 56, 59, 60, 66, 67, 69
Part a
The range is calculated as the difference between the maximum and minimum observations of a sample. To determine those values you need the sample ordered from least to greatest.
For group 1:
Minimum value: 33 words/min
Maximum value: 67 words/min
Range= maximum-minimum=67-33=34words/min
For group 2:
Minimum value: 33words/min
Maximum value: 69 words/min
Range: 69-33=36words/min
→ the range for group 1 is 34words/min while the range for group 2 is 36words/min
Part b
To determine which group had more typing speeds in the fourties you have to count said observations for both of them.
You can do it directly from the stem and leaf plot, go to the row correpsonding to the 4 in the plot and count or use the values:
For group 1: in the second row there are 8 leafs, corresponding to the observations: 42, 44, 44, 45, 47, 48, 49, 49,
For group 2: in the second row there are 5 leafs, corresponding to the observations: 41, 42, 44, 46, 46
→There are more typing speeds in the 40s in group 1.
Part c:
The median is a measure of center that divides the sample in two halves. To calculate it you have to determine its position and then look for the corresponding value in the sample that was previously ordered from least to greatest.
To determine the position of the mean you have to use the following fomula:
For even samples: n/2
For odd samples: (n+1)/2
Median of group 1
n1=20 students
The sample is even, calculate its position using the first formula:
Position: n/2 = 20/2= 10
The median is in the tenth position, look in the sample for the tenth observation:
33, 34, 37, 42, 44, 44, 45, 47, 48, 49, 49, 50, 51, 52, 52, 55, 55, 63, 66, 67
→The median typing speed for group 1 is 49 words/min
Median of group 2
n2=19 students
The sample is odd, you have to use the second formula to find its position:
Position: (n+1)/2= (19+1)/2= 20/2= 10
The median of this group is the 10th observation:
33, 36, 41, 42, 44, 46, 46, 51, 52, 52, 52, 53, 53, 56, 59, 60, 66, 67, 69
→The median typing speed for group 2 is 52 words/min
→Group 2 has the greater median typing speed.
