Stem and Leaf Diagrams

Use the last leaf on the bottom row, and the key to read it.

Every leaf on the row with stem 3 stands for a time in the thirties.

Look for the leaf that appears most often on the same row.

Range = largest value − smallest value; use the key to read each one.

With 15 values in order, the median is the 8th value.

Each leaf stands for one student, so count every leaf, including repeated ones.

1. Count the leaves on each row: 4, 6, 4 and 2.
2. 4+6+4+2=16
3. Answer: 16 students.

With 12 values, the median is halfway between the 6th and 7th values.

1. There are 12 speeds, so the median is halfway between the 6th and 7th values.
2. In order: 32,\ 35,\ 38,\ 41,\ 41,\ 46,\ 49,\ \ldots
3. The 6th value is 46 and the 7th value is 49.
4. Median =\frac{46+49}{2}=47.5
5. Answer: 47.5 miles per hour.

Read the key carefully: the leaf is the digit after the decimal point.

1. The key shows 5\mid2 means 5.2 seconds.
2. Smallest time: 4.7 seconds. Largest time: 7.4 seconds.
3. Range =7.4-4.7=2.7
4. Answer: 2.7 seconds.

1 metre is 100 cm and 2 metres is 200 cm. Which key gives heights between those?

1. The heights are between 100 cm and 200 cm.
2. The stem gives the hundreds and tens, and the leaf gives the units: 15\mid2 is 152 cm.
3. Answer: Key: 15\mid2 represents 152 cm.

List the ages in the thirties in order from smallest to largest.

1. The ages in the thirties are 31,\ 35,\ 38,\ 31,\ 33.
2. In order: 31,\ 31,\ 33,\ 35,\ 38, so the leaves are 1,\ 1,\ 3,\ 5,\ 8.
3. The missing leaf is 5 (for the age 35).
4. Answer: 5.

Find every mark in the seventies. Keep repeated marks, write only the units digit and put them in order.

1. The marks in the seventies are 75,\ 71,\ 75,\ 79,\ 73.
2. In order: 71,\ 73,\ 75,\ 75,\ 79.
3. The leaves are the units digits, and 75 appears twice: 1\ 3\ 5\ 5\ 9.
4. Answer: 7\mid1\ 3\ 5\ 5\ 9

Count the people who took more than 40 minutes, and put that number over the total.

1. Times more than 40 minutes are on the rows with stems 4 and 5: 5+6=11 people.
2. No one took exactly 40 minutes.
3. Probability =\frac{11}{20}
4. Answer: \frac{11}{20}

Check the key, count the leaves, then check each row is in order.

1. There is a key, and there are 11 leaves, so no number is missing.
2. The row with stem 2 reads 5\ 2\ 9\ 1\ 6, which is not in order.
3. It should be 1\ 2\ 5\ 6\ 9.
4. Answer: the leaves in the row with stem 2 are not in order.

Count the people aged 30 or more (remember 30 counts), then write that number out of 25 as a percentage.

1. Ages of 30 or more are on the rows with stems 3 and 4: 6+4=10 people.
2. \frac{10}{25}=\frac{40}{100}
3. Answer: 40%.

Write out all 10 values using the key, add them, then divide by 10.

1. The values are 15,\ 18,\ 20,\ 22,\ 23,\ 26,\ 27,\ 31,\ 34,\ 34.
2. Total: 15+18+20+22+23+26+27+31+34+34=250
3. Mean: 250\div10=25
4. Answer: 25 press-ups.

Find which value in order is the median, then use the smallest mark and the range to find the largest mark.

Part (a)

1. There are 11 marks, so the median is the 6th mark.
2. In order: 29,\ 34,\ 37,\ 42,\ 48, then the 6th mark is the one with leaf a in the row with stem 5.
3. The median is 54, so a =4.

Part (b)

1. The smallest mark is 29.
2. Largest mark =29+38=67
3. 67 is in the row with stem 6, so b =7.

Use the stems 9, 10, 11, 12 and 13, and put the leaves on each row in order before you count along.

Part (a)

1. The ordered diagram is 9\mid3\ 6\ 6\ 9, 10\mid2\ 4\ 7\ 8, 11\mid0\ 4\ 7\ 8, 12\mid1\ 5, 13\mid4.
2. There are 15 lengths, so the median is the 8th.
3. In order: 93,\ 96,\ 96,\ 99,\ 102,\ 104,\ 107,\ 108
4. Median: 108 minutes.

Part (b)

1. Shortest: 93 minutes. Longest: 134 minutes.
2. Range =134-93=41 minutes.

With 10 values the median is halfway between the 5th and 6th. With 11 values it is the 6th.

Part (a)

1. In order: 14,\ 17,\ 19,\ 23,\ 23,\ 26,\ 28,\ 32,\ 35,\ 39.
2. The 5th and 6th scores are 23 and 26.
3. Median =\frac{23+26}{2}=24.5

Part (b)

1. Now there are 11 scores, so the median is the 6th score.
2. 14,\ 17,\ 19,\ 23,\ 23,\ 26,\ \ldots: the 6th score is 26.

Part (c)

1. Range before: 39-14=25
2. Range after: 45-14=31
3. Increase: 31-25=6

Find the median and range for Surgery A first, then compare each one with Surgery B.

Part (a)

1. There are 15 times, so the median is the 8th.
2. In order: 5,\ 8,\ 9,\ 10,\ 12,\ 14,\ 14,\ 16,\ \ldots
3. Median: 16 minutes.

Part (b)

1. The stem 0 row holds times under 10 minutes, so the shortest time is 5 minutes.
2. Longest: 32 minutes.
3. Range =32-5=27 minutes.

Part (c)

1. Medians: Surgery A 16 minutes, Surgery B 18 minutes, so Surgery A had shorter waits on average.
2. Ranges: Surgery A 27 minutes, Surgery B 31 minutes, so the times at Surgery A were less spread out (more consistent).

For part (b), first work out how many students are in the top 20%.

Part (a)

1. Marks of 40 or more are on the rows with stems 4, 5 and 6 (the two marks of 40 count).
2. 6+6+4=16 students.

Part (b)

1. 20% of 25 is \frac{20}{100}\times25=5 students.
2. The five highest marks are 68,\ 65,\ 64,\ 62,\ 59.
3. The lowest of these is 59.
4. Answer: 59.