how to find range in stem and leaf plots

2: Stanch-&-Leaf Plots, Frequency Tables, and Histograms

Stem-and-Folio Plots
Frequency Tables
� Altogether Data � Uniform Class Intervals � Nonuniform Class Intervals
Histograms

Stem turn-and-Leaf Plots

The stem-and-leaf secret plan is an excellent direction to start an psychoanalysis. To construct a halt-and-leaf plot:

(A) Draw a stemlike axis that covers the range of potential values.
(B) Round the data to two or three significant digits.
(C) Separate each data-point into a stem portion and leaf component. The stanch portion consists of all but the rightmost finger's breadth; the leaf component consists of the right digit.
(D) Place apiece riffle value adjacent to its related to stem value, one leaf happening top of the other.

To instance stem-and-leaf plots, let us look at a data coiffur with the following numerical values:

21, 42, 5, 11, 30, 50, 28, 27, 24, 52

To start, haulage a stem-like axis that extends from the data set's minimum to its level bes:

|5| |4| |3| |2| |1| |0| (x 10)

An axis multiplier (x 10) is included to allow the viewer to decipher the prize of each data point.

The rightmost figure of all data show (the "leaf") is and then plotted against the stemlike axis. For example, a appreciate 21 is aforethought as:

|5| |4| |3| |2|1 |1| |0| (x 10)

The remaining data points are plotted:

|5|02 |4|2 |3|0 |2|1874 |1|1 |0|5 (x 10)

Data are at once sorted in approximate rank order, and the shape, location and spread of the statistical distribution are evident. I'm going to flip the stem-and-leaf to a horizontal orientation to better display these features.

The location of the data stool be summarized by its center. For example, the centerfield of the above stem-and-leaf plot is located between 20 and 30.

4 7 8 2 5 1 1 0 2 0 ------------ 0 1 2 3 4 5 ------------ ^ Center

The spread of the statistical distribution is seen as the dispersion of values around the distribution's center.

4 7 8 2 5 1 1 0 2 0 ------------ 0 1 2 3 4 5 ------------ <----|----> Spread

The physical body of the distribution can be seen as a "skyline silhouette" of the information.

X X X X X X X X X X ------------ 0 1 2 3 4 5 ------------

Notice the "skyscraper" in the middle of the distribution. This peak represents the distribution's "mode." The modality of this particular data kick in the interval 20 to 30. As wel notice that the data demonstrate jolly-good symmetry around the mood. (Nothing is perfect in statistics, especially when the sample is pocket-size.)

With a little apply, a distribution's shape, location, and spread can be envisioned through the stem-and-leaf game.

Forward Demonstrative Example of a Stem-and-Leaf Plot of ground: The next illustrative exemplar shows how a stem-and-leaf patch can be restricted to admit data that power not straight off lend itself to this type of diagram. Turn over this new data set:

1.47, 2.06, 2.36, 3.43, 3.74, 3.78, 3.94

These data have 3 significant digits and a decimal point. In such instances, we first labialize the data to two significant digits. The data set annulate to two portentous digits is: {1.5, 2.1, 2.4, 3.4, 3.7, 3.8, 3.9}. When plotting these points, denary points are ignored. Using root values of 1, 2, and 3, we plot:

|1|5 |2|14 |3|4789 (x 1)

Realizing that this plot is somewhat squashed, we could spread it proscribed past cacophonic the stem using duple values with the first value backward for leaf-values between 0 and 4 and the second stem-value distant for leaf-values between 5 and 9. Here's the indistinguishable data with repeat stem-values:

|1| |1|5 |2|14 |2| |3|4 |3|789 (x 1)

This shows that there is more than one correct way to game a staunch-and-leaf diagram for a given information set.

SPSS: To create a stem-and-flick plot in SPSS, click on Statistics | Summarize | Search and select the variable you want a stem-and-leaf plot of in the "Dependent List" dialogue loge.

Relative frequency Tables

Unclothed Information

It is oft useful to view data in the form of a frequency table. Frequency tables may include three different types of frequencies. These are:

Frequency counts: The number of times a treasure occurs in a data ready.
Proportionate frequencies: Frequencies hardcore as percentages of the total.
Cumulative frequencies: Relative frequencies up to and including the current downright-ordered value.

An example of a table of AGE frequencies is:

Table 1. Age (in years), respiratory health survey respondents.

Maturat | Freq Rel.Freq Cum.Freq. ------+----------------------- 3 | 2 0.3% 0.3% 4 | 9 1.4% 1.7% 5 | 28 4.3% 6.0% 6 | 37 5.7% 11.6% 7 | 54 8.3% 19.9% 8 | 85 13.0% 32.9% 9 | 94 14.4% 47.2% 10 | 81 12.4% 59.6% 11 | 90 13.8% 73.4% 12 | 57 8.7% 82.1% 13 | 43 6.6% 88.7% 14 | 25 3.8% 92.5% 15 | 19 2.9% 95.4% 16 | 13 2.0% 97.4% 17 | 8 1.2% 98.6% 18 | 6 0.9% 99.5% 19 | 3 0.5% 100.0% ------+----------------------- Total | 654 100.0%

To create a frequency table:

(A) List all potential values in upward order

(B) Tally relative frequency counts (f_i ) with tick First Baron Marks of Broughton or some unusual accounting mechanism. List these frequencies in the Freq column of the table.

(D) Calculate relative frequencies (percentages) for each value (p_i = f_i / n).

(E) Calculate cumulative frequencies by adding the cumulative frequency from the prior storey to the frequency of the current story (c_i = p_i + c_i _-1).

SPSS: To create a frequence table in SPSS, click on Statistics | Sum up | Frequencies and select the variable you want a frequency table of in the "Variable(s):" duologue box.

Every bit an additional illustration, let us reconsider the data set {21, 42, 5, 11, 30, 50, 28, 27, 24, 52}. A frequence table for this information set is:

Value Talley Freq. RelFreq CumFreq ------ ------ ----- -------- ------- 5 / 1 10% 10% 11 / 1 10% 20 21 / 1 10% 30% 24 / 1 10% 40% 27 / 1 10% 50% 28 / 1 10% 60% 30 / 1 10% 70% 42 / 1 10% 80% 50 / 1 10% 90% 52 / 1 10% 100% ------------------------------------------ TOTAL 10 100% --

Because of the minute size of the sample, this frequency table is not particularly useful. For it to get ahead more useful, data must be grouped into class intervals.

Uniform Grade Intervals

It is often difficult to learn much by superficial at a frequency listing of values when the dataset is small so that all prise in the information set appears only once Oregon twice. To address this problem, we condense the data into class interval groupings.

There are no sticky-and-fast rules for determining appropriate class intervals. Nevertheless, Here are some rules-of-pollex by which to begin:

(A) Decide on an appropriate add up of course of instruction-interval groupings: The optimum number of assort groupings will look on the range of values and the size of the data set. In general, banging data sets can support a multitude of class groupings and small information sets can back up fewer. Deciding on a suited turn of class-intervals may require several trial and error. To start, attempt class-intervals that are of equal and convenient length (e.g., 10-year old age intervals) or undergo substantive significant (e.g., hypotensive / normotensive / minimum hypertensive / hypertensive). Normally, 4 to 12 division-intervals is usually sufficient.

(B) Determine the class interval width. This can be ambitious with the rule:

Class-interval width = (maximum value - minimum value) / (no more. of desired class groupings)

For example, to create 8 class groupings for a information set with a maximum of 19 and stripped-down of 3, the class interval width = (19 - 3) / 8 = 2.

(C) Set endpoint conventions. If an observation falls on the bounds between two class intervals, we call for know in which course of instruction interval it will be counted. The cardinal choices are to: (a) include the left boundary and exclude the right boundary operating room (b) include the the right way bound and exclude the left boundary. When moon-faced with this choice, we will role the option "a". For example, when considerateness a two social unit time interval of 2 to 4, we leave chuck out the suited bound of 4, then that the interval is between 2 (inclusive) up to 4 (sole).

(D) Tabulate the data: Once boundaries are established, the data are counted in the usual way.

A frequence table for the small data set {21, 42, 5, 11, 30, 50, 28, 27, 24, 52} with 15-year age class-time interval grouping can now e shown:

Stray Tally Freq. RelFreq CumFreq ------ ------ ----- -------- ------- 0-14 // 2 20% 20% 15-29 //// 4 40% 60% 30-44 // 2 20% 80% 45-54 // 2 20% 100% ------------------------------------------ TOTAL 10 100% --

SPSS: To group data in SPSS, get across happening Translate | Recode | Into Different Variable. This will leave you to raise ranges to serve as class intervals. After recoding the data to these new class intervals (ranges), a Statistics | Summarize | Frequencies program line can be directed against the newly recoded inconstant.

Nonuniform Class Intervals

At times we might require to use nonuniform grade-intervals when describing frequencies. For instance, we may want to take age distribution of children with ages sorted as preschool (2-4 age), elementary school (5-11-days), middle-civilis (12-13-geezerhood), and highschool (14-19-years). The data from Table 1 can directly be displayed as follows:

Histograms

The research worker may choose to graphically review frequencies in the form of a histogram. Histograms are bar charts that presentation frequencies Oregon relative frequencies in the form of contiguous (touching) bars. A histogram of the eld dispersion information (before it was condensed into class intervals) is shown in the figure to the right:

SPSS: To create a histogram, click happening Graphs | Histogram. To create a frequence polygon with SPSS, detent on Graphs | Crease | Define, and and so select the variable you want to graph in the Category Axis dialogue box. (The line will represent the identification number of cases, by default.)

Note

n - sample size
f_i = frequency, value or interval i
p_i = frequency, value or time interval i
c_i = cumulative frequency, time value or interval i

Mental lexicon

Cumulative frequency: the accumulation of relative frequencies up to and including the social rank-ordered economic value or class.
Frequency: the phone number of times a fussy item occurs.
Histogram: a bar graph of frequencies OR relative frequencies in which bars hint.
Relative absolute frequency: frequencies expressed as a percentage of the absolute.
Stem-and-foliage plot: a histogram-like display of injured values in a data set.

how to find range in stem and leaf plots

Source: https://www.sjsu.edu/faculty/gerstman/StatPrimer/freq.htm

Rose Betion1973