according to the plot above, what is the period?

Stem and foliage plots

Archived Content

Information identified as archived is provided for reference, research or recordkeeping purposes. Information technology is not bailiwick to the Authorities of Canada Spider web Standards and has not been altered or updated since information technology was archived. Delight contact usa to asking a format other than those bachelor.

• Elements of a good stem and leaf plot
• Tips on how to draw a stem and leaf plot
  • Example ane – Making a stem and leaf plot
• The chief reward of a stem and foliage plot
  • Example 2 – Making a stem and leafage plot
  • Example 3 – Making an ordered stem and leaf plot
• Splitting the stems
  • Example 4 – Splitting the stems
  • Instance 5 – Splitting stems using decimal values
• Outliers
• Features of distributions
• Using stem and leaf plots as graphs
  • Case six – Using stem and leaf plots as graph

A stem and foliage plot, or stem plot, is a technique used to allocate either detached or continuous variables. A stem and leaf plot is used to organize information equally they are collected.

A stalk and leaf plot looks something like a bar graph. Each number in the information is broken down into a stem and a leaf, thus the name. The stem of the number includes all but the terminal digit. The leafage of the number will ever exist a single digit.

Elements of a good stalk and leaf plot

A proficient stem and leaf plot

• shows the first digits of the number (thousands, hundreds or tens) as the stalk and shows the final digit (ones) equally the leaf.
  
• usually uses whole numbers. Anything that has a decimal bespeak is rounded to the nearest whole number. For case, test results, speeds, heights, weights, etc.
  
• looks similar a bar graph when it is turned on its side.
  
• shows how the information are spread—that is, highest number, lowest number, nigh common number and outliers (a number that lies outside the primary group of numbers).

Top of Page

Tips on how to describe a stem and leaf plot

Once yous accept decided that a stem and leaf plot is the best manner to show your data, draw information technology every bit follows:

• On the left manus side of the folio, write downwardly the thousands, hundreds or tens (all digits merely the terminal one). These will be your stems.
• Draw a line to the right of these stems.
• On the other side of the line, write down the ones (the final digit of a number). These will be your leaves.

For example, if the observed value is 25, then the stalk is 2 and the leaf is the 5. If the observed value is 369, so the stem is 36 and the leaf is ix. Where observations are authentic to ane or more decimal places, such as 23.7, the stalk is 23 and the leaf is 7. If the range of values is too bang-up, the number 23.seven can be rounded up to 24 to limit the number of stems.

In stem and leaf plots, tally marks are not required because the actual data are used.

Non quite getting it? Try some exercises.

Example 1 – Making a stem and leaf plot

Each morning, a teacher quizzed his class with 20 geography questions. The class marked them together and anybody kept a record of their personal scores. As the year passed, each student tried to improve his or her quiz marks. Every twenty-four hours, Elliot recorded his quiz marks on a stem and leaf plot. This is what his marks looked similar plotted out:

Table i. Elliot's scores on the basic facts quiz last year

Stalk	Leafage
0	3 6 5
1	0 1 iv 3 five 6 5 vi eight 9 7 nine
2	0 0 0 0

Analyse Elliot's stem and leaf plot. What is his nearly common score on the geography quizzes? What is his highest score? His lowest score? Rotate the stem and leafage plot onto its side and so that it looks like a bar graph. Are virtually of Elliot's scores in the 10s, 20s or under 10? It is difficult to know from the plot whether Elliot has improved or not because nosotros exercise not know the order of those scores.

Try making your own stem and leaf plot. Use the marks from something like all of your exam results terminal year or the points your sports squad accumulated this flavour.

Top of Page

The primary advantage of a stem and foliage plot

The main advantage of a stem and foliage plot is that the data are grouped and all the original information are shown, too. In Example three on bombardment life in the Frequency distribution tables section, the table shows that two observations occurred in the interval from 360 to 369 minutes. However, the tabular array does not tell you what those actual observations are. A stem and leaf plot would show that information. Without a stem and leaf plot, the 2 values (363 and 369) tin only exist plant past searching through all the original data—a tedious task when you have lots of data!

When looking at a data set, each observation may be considered equally consisting of two parts—a stem and a foliage. To brand a stem and leaf plot, each observed value must offset be separated into its two parts:

• The stalk is the first digit or digits;
• The leaf is the final digit of a value;
• Each stem can consist of any number of digits; but
• Each leaf tin can have only a single digit.

Elevation of Page

Instance 2 – Making a stem and leaf plot

A teacher asked 10 of her students how many books they had read in the last 12 months. Their answers were as follows:

12, 23, nineteen, 6, 10, 7, 15, 25, 21, 12

Prepare a stem and leaf plot for these data.

Tip: The number 6 can exist written equally 06, which means that information technology has a stalk of 0 and a leaf of vi.

The stem and leaf plot should look like this:

Tabular array two. Books read in a year past 10 students

Stem	Leaf
0	half dozen 7
1	two 9 0 five ii
2	3 v 1

In Table two:

• stem 0 represents the course interval 0 to 9;
• stem 1 represents the class interval ten to xix; and
• stalk 2 represents the class interval 20 to 29.

Normally, a stalk and leafage plot is ordered, which simply means that the leaves are arranged in ascending society from left to right. Also, in that location is no demand to carve up the leaves (digits) with punctuation marks (commas or periods) since each leaf is always a unmarried digit.

Using the data from Tabular array 2, we fabricated the ordered stem and leaf plot shown below:

Tabular array 3. Books read in a year by 10 students

Stalk	Leaf
0	6 7
i	0 2 2 5 ix
2	1 three five

Meridian of Folio

Example iii – Making an ordered stem and leafage plot

15 people were asked how often they drove to work over x working days. The number of times each person drove was as follows:

v, vii, nine, 9, 3, v, ane, 0, 0, 4, 3, vii, 2, ix, 8

Make an ordered stem and foliage plot for this table.

It should exist drawn as follows:

Table 4. Number of drives to work in 10 days

Stem	Leafage
0	0 0 1 2 3 three 4 5 5 vii 7 8 9 9 9

Splitting the stems

The organisation of this stem and leafage plot does not give much data almost the data. With only 1 stem, the leaves are overcrowded. If the leaves become also crowded, so information technology might be useful to carve up each stem into two or more components. Thus, an interval 0–ix can exist split into two intervals of 0–four and v–9. Similarly, a 0–9 stalk could exist split into five intervals: 0–1, 2–3, 4–5, 6–7 and 8–nine.

The stem and leaf plot should and so look like this:

Tabular array 5. Number of drives to work in ten days

Stem	Leaf
0(0)	0 0 1 ii three iii iv
0(5)	5 5 7 seven 8 ix nine 9

Note: The stem 0⁽⁰⁾ means all the information within the interval 0–4. The stalk 0^(five) means all the information inside the interval 5–ix.

Top of Page

Example 4 – Splitting the stems

Britney is a swimmer training for a competition. The number of l-metre laps she swam each day for xxx days are as follows:

22, 21, 24, xix, 27, 28, 24, 25, 29, 28, 26, 31, 28, 27, 22, 39, 20, 10, 26, 24, 27, 28, 26, 28, 18, 32, 29, 25, 31, 27

1. Ready an ordered stem and leafage plot. Make a brief comment on what it shows.
2. Redraw the stem and foliage plot by splitting the stems into v-unit intervals. Make a brief comment on what the new plot shows.

Answers

1. The observations range in value from ten to 39, so the stem and leaf plot should take stems of 1, two and iii. The ordered stem and leaf plot is shown beneath:

   Tabular array 6. Laps swum by Britney in 30 days

   Stem	Leaf
   i	0 viii 9
   two	0 ane 2 two 4 4 iv five 5 vi 6 6 vii vii 7 seven viii 8 8 8 8 ix nine
   3	1 1 ii 9

   The stem and leafage plot shows that Britney usually swims between 20 and 29 laps in training each day.
2. Splitting the stems into v-unit intervals gives the post-obit stem and foliage plot:

   Tabular array vii. Laps swum by Britney in thirty days

   Stem	Leaf
   1(0)	0
   i(5)	8 9
   ii(0)	0 1 two 2 iv four 4
   ii(5)	five 5 six 6 six 7 vii 7 7 viii 8 8 8 eight ix 9
   3(0)	1 1 ii
   3(five)	nine

   Note: The stem 1⁽⁰⁾ means all data between ten and 14, 1⁽⁵⁾ means all information between 15 and 19, so on.

   The revised stem and foliage plot shows that Britney usually swims between 25 and 29 laps in preparation each twenty-four hours. The values one⁽⁰⁾ 0 = 10 and 3^(five) ix = 39 could exist considered outliers—a concept that will be described in the adjacent section.

Top of Page

Example 5 – Splitting stems using decimal values

The weights (to the nearest tenth of a kilogram) of 30 students were measured and recorded as follows:

59.two, 61.5, 62.3, 61.4, threescore.ix, 59.8, threescore.5, 59.0, 61.1, 60.7, 61.6, 56.three, 61.9, 65.7, sixty.4, 58.9, 59.0, 61.2, 62.one, 61.iv, 58.4, lx.8, threescore.2, 62.7, 60.0, 59.3, 61.9, 61.7, 58.iv, 62.2

Prepare an ordered stalk and leaf plot for the data. Briefly annotate on what the analysis shows.

Answer

In this case, the stems will exist the whole number values and the leaves will be the decimal values. The information range from 56.three to 65.7, so the stems should kickoff at 56 and finish at 65.

Table viii. Weights of 30 students

Stem	Leaf
56	three
57
58	four 4 nine
59	0 0 two 3 viii
threescore	0 2 four 5 7 8 ix
61	1 2 four 4 v 6 7 ix 9
62	1 2 three seven
63
64
65	7

In this case, information technology was not necessary to split stems because the leaves are not crowded on too few stems; nor was it necessary to circular the values, since the range of values is not large. This stem and leaf plot reveals that the group with the highest number of observations recorded is the 61.0 to 61.ix group.

Top of Page

Outliers

An outlier is an farthermost value of the data. It is an observation value that is significantly different from the residual of the information. In that location may be more than than ane outlier in a prepare of information.

Sometimes, outliers are significant pieces of information and should not exist ignored. Other times, they occur because of an mistake or misinformation and should be ignored.

In the previous example, 56.3 and 65.vii could be considered outliers, since these two values are quite dissimilar from the other values.

By ignoring these two outliers, the previous example's stalk and leaf plot could be redrawn as beneath:

Tabular array ix. Weights of 30 students except for outliers

Stem	Leaf
58	4 4 nine
59	0 0 ii 3 8
lx	0 2 four v seven 8 9
61	1 two four iv 5 half-dozen vii 9 9
62	1 2 3 7

When using a stem and leaf plot, spotting an outlier is often a matter of judgment. This is because, except when using box plots (explained in the department on box and whisker plots), in that location is no strict rule on how far removed a value must be from the rest of a data set up to qualify as an outlier.

Summit of Page

Features of distributions

When y'all assess the overall pattern of any distribution (which is the blueprint formed by all values of a particular variable), look for these features:

• number of peaks
• general shape (skewed or symmetric)
• heart
• spread

Number of peaks

Line graphs are useful because they readily reveal some characteristic of the data. (See the section on line graphs for details on this blazon of graph.)

The showtime characteristic that tin can be readily seen from a line graph is the number of high points or peaks the distribution has.

While most distributions that occur in statistical information accept only one main peak (unimodal), other distributions may take two peaks (bimodal) or more than 2 peaks (multimodal).

Examples of unimodal, bimodal and multimodal line graphs are shown beneath:

General shape

The second primary feature of a distribution is the extent to which it is symmetric.

A perfectly symmetric curve is i in which both sides of the distribution would exactly lucifer the other if the effigy were folded over its central point. An example is shown beneath:

A symmetric, unimodal, bong-shaped distribution—a relatively mutual occurrence—is called a normal distribution.

If the distribution is lop-sided, it is said to be skewed.

A distribution is said to be skewed to the correct, or positively skewed, when nigh of the information are concentrated on the left of the distribution. Distributions with positive skews are more than common than distributions with negative skews.

Income provides 1 instance of a positively skewed distribution. Virtually people make under $twoscore,000 a year, but some make quite a bit more, with a smaller number making many millions of dollars a year. Therefore, the positive (right) tail on the line graph for income extends out quite a long fashion, whereas the negative (left) skew tail stops at nix. The correct tail clearly extends farther from the distribution's centre than the left tail, every bit shown below:

A distribution is said to be skewed to the left, or negatively skewed, if most of the data are concentrated on the correct of the distribution. The left tail clearly extends further from the distribution'southward centre than the right tail, as shown below:

Centre and spread

Locating the center (median) of a distribution tin be done by counting half the observations upwards from the smallest. Obviously, this method is impracticable for very big sets of data. A stem and leafage plot makes this easy, nevertheless, because the data are arranged in ascending club. The mean is another mensurate of central trend. (See the chapter on central tendency for more detail.)

The amount of distribution spread and any large deviations from the general pattern (outliers) can exist quickly spotted on a graph.

Using stem and leafage plots as graphs

A stem and foliage plot is a simple kind of graph that is fabricated out of the numbers themselves. It is a means of displaying the main features of a distribution. If a stem and leafage plot is turned on its side, it will resemble a bar graph or histogram and provide like visual data.

Tiptop of Page

Example 6 – Using stem and foliage plots as graph

The results of 41 students' math tests (with a best possible score of seventy) are recorded below:

31, 49, 19, 62, 50, 24, 45, 23, 51, 32, 48, 55, threescore, 40, 35, 54, 26, 57, 37, 43, 65, fifty, 55, xviii, 53, 41, 50, 34, 67, 56, 44, four, 54, 57, 39, 52, 45, 35, 51, 63, 42

1. Is the variable discrete or continuous? Explain.
2. Prepare an ordered stalk and leaf plot for the data and briefly draw what it shows.
3. Are there any outliers? If so, which scores?
4. Wait at the stalk and leafage plot from the side. Depict the distribution's master features such equally:
   1. number of peaks
   2. symmetry
   3. value at the centre of the distribution

Answers

1. A test score is a discrete variable. For example, it is non possible to have a examination score of 35.74542341....
2. The everyman value is 4 and the highest is 67. Therefore, the stem and leaf plot that covers this range of values looks like this:
   

   Table 10. Math scores of 41 students

   Stem	Leaf
   0	four
   i	8 9
   two	iii four 6
   three	1 2 iv v v 7 ix
   4	0 1 ii 3 4 5 5 8 9
   5	0 0 0 1 1 2 3 4 4 v 5 6 seven vii
   6	0 ii iii 5 7

   Note: The notation 2|4 represents stalk 2 and leaf 4.

   The stem and leaf plot reveals that most students scored in the interval between 50 and 59. The large number of students who obtained high results could mean that the test was too piece of cake, that near students knew the material well, or a combination of both.

3. The issue of 4 could be an outlier, since there is a big gap between this and the next result, 18.
4. If the stalk and leaf plot is turned on its side, it will expect like the following:

   

   The distribution has a single peak inside the 50–59 interval.

   Although in that location are only 41 observations, the distribution shows that most data are clustered at the correct. The left tail extends further from the data centre than the correct tail. Therefore, the distribution is skewed to the left or negatively skewed.

   Since there are 41 observations, the distribution centre (the median value) will occur at the 21st observation. Counting 21 observations up from the smallest, the centre is 48. (Note that the same value would have been obtained if 21 observations were counted downwards from the highest observation.)

schreinersteened1981.blogspot.com

Source: https://www150.statcan.gc.ca/n1/edu/power-pouvoir/ch8/5214816-eng.htm

Share this post