Answer :
The answer provides a stem-and-leaf display for the data and calculates the median and quartiles. It offers a clear step-by-step explanation to help understand the concepts.
a. Stem-and-leaf display:
32 | 0 1 1 2 2 4 4 5 5 5 8 8 8 8 9 9
33 | 0 0 2 2 2 5 5 6 6 6 8 8 8
34 | 0 0 0 1 1 3 3 4 4 5 5 5 6 6 6 6 7 7 7 7 9
35 | 0 0 1 1 1 2 2 4 5 5 5 5 6
36 | 1 3 4 4 5 5 6 7 7
37 | 0 0 1 4 4 6
b. Median and Quartiles:
Sorted data: 32.0, 32.1, 32.1, 32.2, ..., 37.6, 37.8, 37.8, 67 values
Median: (67+1)/2 = 34th value = 34.1%
Q1: (25+1)/4 = 17th value = 33.8%
Q3: 3(25+1)/4 = 51st value = 35.5%
Answer:
Median = 34.55
Quartiles:
Q1 = 33.1
Q2 = 34.55
Q3 = 35.6
Inter Quartile range = 2.5
Step-by-step explanation:
Step 1
We arrange the given the following data from lowest to the highest
32.0, 32.1, 32.1, 32.2, 32.4, 32.5, 32.5, 32.5, 32.8, 32.8, 32.8, 32.8, 32.9, 32.9, 33.0, 33.0, 33.2, 33.2, 33.2, 33.2, 33.5, 33.6, 33.8, 33.8, 33.9, 34.0, 34.0, 34.1, 34.1, 34.3, 34.4, 34.5, 34.6, 34.6, 34.6, 34.7, 34.7, 35.0, 35.0, 35.1, 35.1, 35.2, 35.4, 35.5, 35.5, 35.5, 35.5, 35.6, 35.6, 36.1, 36.3, 36.4, 36.4, 36.4, 36.5, 36.6, 36.7, 36.7, 37.0, 37.1, 37.4, 37.4, 37.6, 37.8
a. Construct a stem-and-leaf display for the data.
Stem and leaf Display
Stem | Leaf
32 | 0,1,1,2,4,5,5,5,8,8,8,8,9,9
33 | 0,0,2,2,2,2,5,6,8,8,9
34 | 0,0,1,1,3,4,5,6,6,6,7,7
35 | 0,0,1,1,2,4,5,5,5,5,6,6,
36 | 1,3,4,4,4,5,6,7,7,
37 | 0,1,4,4,6,8
b. Calculate the median and quartiles of these data.
Number of terms = 64
1) Median = 1/2(n + 1)th value
n = 64
= 1/2(64 + 1)th
= 1/2(65)th
= 32.5 th value
This means it is between the 32nd and 33rd value
32nd = 34.5
33rd = 34.6
= 34.5 + 34.6/2
= 69.1/2
= 34.55
2) First Quartile
1/4(n + 1)th value
n = 64
= 1/4(64 + 1)th
= 1/4(65)th
= 16.5th value
This means it is between the 16th and 17th value
16th value = 33.0
17tj value = 33.2
= 33.0 + 33.2/2
= 66.2/2
= 34.55
Q1 --> 33.1
3)Second Quartile = Median
1/2(n + 1)th value
n = 64
= 1/2(64 + 1)th
= 1/2(65)th
= 32.5 th value
This means it is between the 32nd and 33rd value
32nd = 34.5
33rd = 34.6
= 34.5 + 34.6/2
= 69.1/2
= 34.55
Q2 --> 34.55
Third Quartile
3/4(n + 1)th value
n = 64
= 3/4(64 + 1)th
= 3/4(65)th
= 48.75 th value
This means it is towards the 49th value
32nd = 34.5
Hence,
Q3 --> 35.6
Inter Quartile range
Q3 - Q1
= 35.6 - 33.1
= 2.5
