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Stem and Leaf Diagram

Stem and Leaf Diagram. People were asked their age as they entered a health centre. Their ages were: 25, 28, 21, 17, 33, 15, 26, 31, 20, 21 and 18. The data recorded can be shown in a stem and leaf diagram also referred to as a Stem Plot. . The title. Ages (Years). The Stem. 5 7 8. 1.

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Stem and Leaf Diagram

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  1. Stem and Leaf Diagram People were asked their age as they entered a health centre. Their ages were: 25, 28, 21, 17, 33, 15, 26, 31, 20, 21 and 18. The data recorded can be shown in a stem and leaf diagram also referred to as a Stem Plot. The title Ages (Years) The Stem 5 7 8 1 The leaves 2 0 1 1 5 6 8 3 1 3 The Key n = 11 1 5 represents 15 years of age

  2. Ages (Years) 5 7 8 1 2 0 1 1 5 6 8 3 1 3 n = 11 1 5 represents 15 years of age • The figures on the left of the line form the stem. • Each figure on the right is called a leaf. • The leaves increase in value outwards from the stem. • Each row is called a level. • A title is needed at the top. • A key is needed at the bottom. A stem and leaf diagram is easier to produce if you order the data first.

  3. Exercise GS1 on page G3.

  4. Books borrowed from the library Last Week This week 3 2 0 1 4 1 3 1 5 6 7 4 4 3 4 0 4 5 1 0 5 2 1 6 3 2 0 represents 20 books n = 10 n = 10 Back to back stem and leaf diagram Sometimes you want to compare one set of figures with another. A back to back stem and leaf diagram is useful The 2 level can be read as “last week there was an opening when 23 books were borrowed and this week there were openings with 20 and 21 books borrowed.” The library opens 10 times a week.

  5. Exercise GS2 on page G5

  6. Frequency Tables The receptionist at a vets surgery notes the types of animals as they are brought in. This kind of table is referred to as a frequency table. She decides to sort the data onto a table.

  7. Exercise GS3 Page G6

  8. Constructing A Pie Chart Geologists carry out a survey on rocks. Here are their results.

  9. 1200 1800

  10. Limestone Granite Sandstone

  11. Exercise CS1 Page C3

  12. Cumulative Frequency The cumulative frequency of age 5 is 24 This can be interpreted as 24 people in the sample aged 5 or less.

  13. Exercise CS2 on page C4

  14. Age In Years (to nearest 5) Frequency Cumulative Frequency 10 5 5 15 7 12 20 12 24 25 32 56 cumulative frequency 30 14 70 35 18 88 40 12 100 Age (years) Cumulative Frequency Diagram 60 Patients are around 25 Years old

  15. Exercise CS3 on page C6

  16. 13 10 11 12 Dotplots It is sometimes useful to get a “feel” for the location of a data set on a number line. One way to do this is to construct a dotplot. A group of athletes are timed in a 100m sprint. Their times are: 10.8, 10.9, 11.2, 11.5, 11.6, 11.6, 11.6, 11.9, 12.2, 12.2, 12.8.

  17. Exercise CS4 on Page C8

  18. The Five Figure Summary When a list of numbers is put in order it can be summarised by quoting five figures. • The highest number (H) • The lowest number (L) • The Median (Q2). This number halves the list and does not belong in either half. • The upper quartile (Q3). The median of the upper half. • The lower quartile (Q1). The median of the lower half.

  19. Give a five figure summary of the following data. 3 5 6 6 7 8 8 8 9 10 11 Q1 Q2 H L Q3 L = 3 Q1 = 6 Q2 = 8 Q3 = 9 H = 11

  20. Give a five figure summary of the following data. 3 5 6 6 7 8 8 9 10 11 Q1 Q2 H L Q3 L = 3 Q1 = 6 Q2 = ( 7 + 8 )  2 = 7.5 Q3 = 9 H = 11

  21. Give a five figure summary of the following data. 3 5 6 6 7 8 9 10 11 Q1 Q2 H L Q3 L = 3 Q1 = ( 5 + 6 )  2 = 5.5 Q2 = 7 Q3 = ( 9 + 10 )  2 = 9.5 H = 11

  22. Exercise CS5 on page C10

  23. Boxplots The five figure summary can be illustrated using a boxplot A boxplot is drawn to a suitable scale and displays the five figure summary as follows. H Q3 Q2 Q1 L A suitable scale

  24. 0 100 80 60 20 40 Example. Lowest score = 12; highest score = 97; Q1 = 32, Q2 = 49, Q3 = 66. For an exam out of 100, the boxplot is: Note that: 25% of the candidates got between 12 and 32 (lower Whisker) 50% of the candidates got between 32 and 66 (in the box) 25% of the candidates got between 66 and 97 (upper whisker)

  25. Exercise CS6 on page C11

  26. Comparing Distributions When comparing distributions it is useful to consider two things: • The typical score (the mean, the mode or the median) • The spread of the marks (the range can be useful, but more often the interquartile range or semi-interquartile range is used)

  27. 56 20 52 38 24 96 11 78 51 32 0 100 80 60 20 40 Boxplots can be used to help compare distributions. January June Comparison of exam results by the same class. On average the June results are better since the median is higher. But scores tended to be more variable. (larger interquartile range) Note that the longer the box, the greater the interquartile range and hence the variability.

  28. Exercise CS7 on page C13.

  29. Calculating the Quartiles To find the quartiles of an ordered list we consider its length.

  30. a) Where are the quartiles in a data list of 24 numbers. 13 TO 18 1 TO 6 19 TO 24 7 TO 12 1 TO 12 13 TO 24 24 numbers can be divided into 2 equal groups of 12 numbers. The median will be between the 12th and 13th numbers The lower quartile will be between the 6th and 7th numbers The upper quartile will be between the 18th and 19th numbers

  31. 14 TO 19 1 TO 6 20 TO 25 7 TO 12 1 TO 12 14 TO 25 b) Where are the quartiles in a data list of 25 numbers. 25 numbers can be divided into 2 equal groups of 12 numbers. The median will be the 13th number The lower quartile will be between the 6th and 7th numbers The upper quartile will be between the 19th and 20th numbers

  32. 14 TO 19 1 TO 6 21 TO 26 8 TO 13 1 TO 13 14 TO 26 c) Where are the quartiles in a data list of 26 numbers. 26 numbers can be divided into 2 equal groups of 13 numbers. The median will be between the 13th and 14th numbers The lower quartile will be the 7th number The upper quartile will be the 20th number

  33. 15 TO 20 1 TO 6 22 TO 27 8 TO 13 1 TO 13 15 TO 27 d) Where are the quartiles in a data list of 27 numbers. 27 numbers can be divided into 2 equal groups of 13 numbers. The median will be the 14th number The lower quartile will be the 7th number The upper quartile will be the 21st number

  34. Exercise CS8 on page C14

  35. Using a Cumulative Frequency Column The frequency table shows the length of commercial breaks in minutes, broadcast on a TV channel one evening. Calculate the median and the quartiles of these times. Data list is 22 numbers long By adding a cumulative frequency column we can see the total data list

  36. 12 TO 16 1 TO 5 18 TO 22 7 TO 11 1 TO 11 12 TO 22 6th number is here 11th and 12th numbers are here 17th number is here 22 numbers can be split into two equal groups of 11 4 mins 4 mins Q2 = Q3 = 3 mins Q1 =

  37. Exercise CS9 on page C16

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