2-1 Stem-and-Leaf Data Representation: practice questions
Unit 2 — Advanced Measurements in Statistics · Statistics. These are 10 questions from the Magmo3 bank on this lesson, from easy to hard. Solve each one, then open "Show answer and explanation". Magmo3 has 87 questions on this lesson, each with an explanation.
One advantage of representing data by the stem-and-leaf method is that ……
Ait does not need the leaves to be ordered
Bit gives the arithmetic mean directly
Cit is suitable for very large data sets
Dit preserves the original data
Show answer and explanation
Correct answer: (D) it preserves the original data
Explanation: Step 1: In a stem-and-leaf plot every value can be read back, unlike a frequency table, where it is not possible to return to the original data.
Step 2: Its disadvantage is that it is not suitable for large data sets.
∴ the advantage is that the original data are preserved.
Question 2Easy
In a stem-and-leaf plot (Key 23 = 2|3): stem 1: 2, 4, 4, 7 — stem 2: 0, 3, 3, 3, 6, 8 — stem 3: 1, 5. The mode of these data = ……
A20
B24
C23
D3
Show answer and explanation
Correct answer: (C) 23
Explanation: Step 1: The mode is the most frequent value.
Step 2: The leaf 3 appears 3 times on stem 2, so 23 appears 3 times; no other value appears more than twice.
∴ mode = 23 (not the leaf 3 alone).
Question 3Easy
In a double stem-and-leaf plot used to compare two data sets ……
Athere is one common stem column, with the leaves of each data set on one side of it
Bthe stem represents the ones digit and the leaves represent the tens digit for both data sets
Cthe leaves of both data sets are written together on the right of the stem after ordering
Deach data set has its own stem column, with its leaves on the right
Show answer and explanation
Correct answer: (A) there is one common stem column, with the leaves of each data set on one side of it
Explanation: Step 1: In a double stem-and-leaf plot the stem is the same for both data sets.
Step 2: The leaves of the first data set are on the right side of the stem, and the leaves of the second data set are on the left side.
∴ one common stem, with the leaves of each data set on one side of it.
Question 4Medium
A stem-and-leaf plot shows the number of mathematics books in the libraries of 13 schools (Key 13 = 1|3): stem 0: 2, 3, 3, 7 — stem 1: 0, 1, 1, 1, 4, 6, 6 — stem 2: 0, 2. The total number of mathematics books in all these libraries = ……
A146
B104
C36
D124
Show answer and explanation
Correct answer: (A) 146
Explanation: Step 1: The original data: 2, 3, 3, 7, 10, 11, 11, 11, 14, 16, 16, 20, 22
Step 2: sum = 146
∴ total = 146 (36 is the sum of the leaves only, and 124 counts 11 once although it appears 3 times).
Question 5Medium
In a double stem-and-leaf plot of two data sets (Key 41 = 4|1) with the leaves in ascending order: stem 3: first set 2, 5 and second set 8 — stem 4: first set 1, 4, 6 and second set 0, x, 7 — stem 5: first set 2, 7 and second set 1. If the arithmetic mean of the second set equals the median of the first set, then x = ……
A3
B6
C4
D1
Show answer and explanation
Correct answer: (C) 4
Explanation: Step 1: First set (7 values): 32, 35, 41, 44, 46, 52, 57, median = the 4th value = 44
Step 2: Second set (5 values): 38, 40, 40 + x, 47, 51, sum = 216 + x
Step 3: (216 + x) ÷ 5 = 44, so 216 + x = 220
∴ x = 4
Question 6Medium
A stem-and-leaf plot shows the numbers of computers in 12 schools (Key 15 = 1|5): stem 0: 6, 8 — stem 1: 2, 2, 5, 9 — stem 2: 0, 4, 4 — stem 3: 1, 3 — stem 4: 0. The administration decided to bring every school that has fewer than 20 computers up to 20 computers. The number of extra computers needed = ……
A48
B40
C22
D34
Show answer and explanation
Correct answer: (A) 48
Explanation: Step 1: Schools with fewer than 20 computers: 6, 8, 12, 12, 15, 19
Step 2: extra computers = 14 + 12 + 8 + 8 + 5 + 1 = 48
∴ 48 (40 counts the school with 12 computers only once, and 22 ignores stem 0).
Question 7Medium
In a stem-and-leaf plot (Key 25 = 2|5): stem 1: 0, 4 — stem 2: 2, 5, 6 — stem 3: 0, 3 — stem 4: 6. The percentage of the values that are greater than the arithmetic mean of these data = ……
A62.5%
B25%
C50%
D37.5%
Show answer and explanation
Correct answer: (C) 50%
Explanation: Step 1: sum = 10 + 14 + 22 + 25 + 26 + 30 + 33 + 46 = 206, so mean = 206 ÷ 8 = 25.75
Step 2: values greater than 25.75: 26, 30, 33, 46, that is 4 of the 8 values.
∴ percentage = 4 ÷ 8 = 50% (37.5% comes from missing 26, which is close to the mean).
Question 8Hard
A stem-and-leaf plot of an odd number of values has three stems: the first stem has 4 leaves and the last stem has 6 leaves. If the median is the third leaf on the middle stem, then the number of leaves on the middle stem = ……
A13
B7
C4
D3
Show answer and explanation
Correct answer: (D) 3
Explanation: Step 1: order of the median = 4 + 3 = 7
Step 2: n is odd, so the order of the median = (n + 1) ÷ 2 = 7, so n = 13
Step 3: leaves on the middle stem = 13 − 4 − 6 = 3
∴ 3 (taking n = 2 × 7 = 14 gives 4; 7 is the order of the median and 13 is the number of all the values).
Question 9Hard
A double stem-and-leaf plot shows the marks of two classes (Key 46 = 4|6): stem 3: first class 5, 8 and second class 1, 4, 9 — stem 4: first class 2, 6, 6 and second class 0, 5, 5, 5 — stem 5: first class 1, 8 and second class 2, 6 — stem 6: first class 3. Which of the following statements is true?
AThe two classes have the same mode
BThe range of the second class is 3 more than the range of the first class
CThe median of the second class is greater, and the range of the first class is greater
DThe median of the first class is greater, and its range is greater
Show answer and explanation
Correct answer: (D) The median of the first class is greater, and its range is greater
Explanation: Step 1: First class (8 marks): median = (46 + 46) ÷ 2 = 46, range = 63 − 35 = 28, mode = 46
Step 2: Second class (9 marks): median = the 5th mark = 45, range = 56 − 31 = 25, mode = 45
∴ the median of the first class is greater and its range is greater (the difference of 3 in the ranges is in favour of the first class, not the second).
Question 10Hard
In a stem-and-leaf plot (Key 25 = 2|5): stem 1: 2, 8 — stem 2: 1, 5, 5 — stem 3: 0, 3. Which of the following values, if added to these data, keeps the median the same and increases the range?
A41
B25
C28
D9
Show answer and explanation
Correct answer: (A) 41
Explanation: Step 1: Now the median = the 4th value = 25 and the range = 33 − 12 = 21
Step 2: After adding a value there are 8 values, so the median is the mean of the 4th and 5th values.
Step 3: Adding 41: the 4th and 5th values are 25 and 25, so the median stays 25 and the range becomes 41 − 12 = 29
∴ 41 (adding 9 increases the range but makes the median (21 + 25) ÷ 2 = 23; adding 25 or 28 keeps the median 25 but does not change the range).