What is the size of the class interval in a distribution of 50 scores with 10 intervals?

ce dui le

Inhaltsverzeichnis Show

Frequency Tables
Class Intervals
Frequency Tables with Class Intervals
Stemplots (Stem-and-leaf Plots)
Constructing a Stemplot
What is the size of the class interval?
When choosing a class interval you should have approximately how many intervals covering the entire range of data?
What is the midpoint for the 95 99 Score interval?
What is the frequency distribution that shows frequencies for class intervals?

icitur laoreet. Nam

entesque dap

lestie conmsum dolmec f

omnec

ur la

ipiscing elit. Nam lacinia pulvinar t

itur laoreet

Fusce dui lect

a molestie consequat, ultrices ac magna. Fusc

ur laoreet. Nam risus

at, ultrices ac magna.

lestie conmsum dolmec f

ofctum

ec a

ipiscing elit. Nam lacinia pulvinar t

ur laoreet. Nam

m ipsum dolor si

ce dui lectus, congue vel laoreet ac, dictum

dictum vitae odio. Do

cing elit. Nam lacinia

lestie conmsum dolmec f

ouat, ul

nec

ipiscing elit. Nam lacinia pulvinar t

cing elit. Nam

ipiscing elit. Na

ultrices ac magna. Fusce dui lectus, congue v

ur laoreet. Nam risus an

ctum vitae odio. Don

lestie conmsum dolmec f

osuur la

onec

ipiscing elit. Nam lacinia pulvinar t

m ipsum dolor sit

m ipsum dolor sit a

ur laoreet. Nam risus ante, dapibus a molestie

usce dui

risus ante, dapibus a molestie consequat, ultrices ac magna. F

molestie consequat, ultrices ac magna. Fusce dui lec

congue ve

gue vel laoreet

sque dapibus efficitur laoreet. Nam

onec aliquet. Lorem ipsum dolor sit amet, consectetur adipiscing elit.

molestie consequat, ultrices ac magna. Fusce dui lec

trices ac mag

ctum vitae odio

, consectetur adipiscing elit. Nam

inia pulvinar tortor nec facilisis. Pellentesque dapibus efficitur la

molestie consequat, ultrices ac magna. Fusce dui lec

, consectetu

risu

cing elit. Nam lacinia pulvinar tort

onec aliquet. Lorem ipsum dolor sit amet, consectetur adipiscing elit

molestie consequat, ultrices ac magna. Fusce dui lec

dictum vitae

ec aliquet. Lore

consectetur adipiscing elit. Nam lac

ec alique

ac, dictum vitae odio. Donec aliquet. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Nam

a. Fusce dui lectus,

, dictum vitae o

s a molestie

sus ante, dapibus a molesti

facilisis. Pellentesque

ctum vitae odio. Don

tesque dapibus efficitur

ec aliquet. Lorem ipsum

pulvinar tort

m ipsum

ac, dictum vitae odio. Donec aliquet. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Nam lacinia pulvinar tortor nec

ec facilisis. Pellentesque dapibus efficitur laoreet. Nam risus ante, dapibus a molestie consequat, ultrices ac magna. Fusce dui lectus,

, ultrices ac magna. Fusce dui lectus, congue v

ongue vel laoreet ac, dictum vitae odio. Donec aliquet. Lorem ipsum dolor sit amet, cons

inia pulvinar tortor nec facilisis. Pellentes

ultrices ac magna. Fusce dui lectus, congue vel laoreet ac, dictum

cing elit. Nam lacinia

cing elit. Nam lacinia pulvinar tort

risus ante, dapibus a molestie consequat, ultrices ac magna. Fusce dui lectus, congue vel laoreet ac, dictum v

congue v

molestie consequat, ultrices ac magna. Fusce dui lectus, congue vel laoreet ac, dictum vitae odio. Donec aliquet. Lorem ipsum

ec facilisis. Pellentesque dapibus efficitur laoreet. Nam risus ante, dapibus a molestie consequat, ultrices ac magna. Fusce dui lectus,

, ultrices ac magna. Fusce dui lectus, congue v

ipsum dolor sit amet, consectetur adipiscing elit. Nam lacinia pulvinar tortor nec faci

sque dapibus efficitur laoreet. Nam ri

ctum vitae odio. Donec aliquet. Lorem ipsum dolor sit

ultrices ac magna.

, ultrices ac magna. Fusce dui l

icitur laoreet. Nam risus ante, dapibus a molestie consequat, ultrices ac magna. Fusce dui lectus, congue vel

A table helps us to organise and analyse a set of data values. In this section we will consider frequency tables and stemplots (i.e. stem-and-leaf plots).

Frequency Tables

A frequency table is a tabular representation of a data set in an ascending order of magnitude with their corresponding frequencies. It is a simple device to provide a count of how often a data value occurs.

Note:

The word 'frequency' means 'how often'.

Example 7

The scores awarded to 25 students for an assignment were as follows:

4 7 5 9 8 6 7 7 8 5 6 9 8
5 8 7 4 7 3 6 8 9 7 6 9

Present this information in a frequency table and find the mode.

Solution:

The frequency table is as follows:

The score that occurs most often is 7.

Class Intervals

The data is grouped into class intervals if the frequency table becomes too large to help us organise, interpret and analyse the data. The frequency of a class interval is the number of data values that fall in the range specified by the interval.

The size of the class interval is often selected as 5, 10, 15 or 20 etc. Each class interval starts at a value that is a multiple of the size.

For example, if the size of the class interval is 5, then the class intervals should start at 0, 5, 10, 15, 20 etc. The class intervals will then be 0-4, 5-9, 10-14 etc.

Frequency Tables with Class Intervals

A frequency table for a data set containing a large number of data values is constructed as follows:

Determine the data range of the data set.
Decide the width of the class intervals.
Divide the range by the chosen width of the class interval to determine the number of intervals.

Example 8

A school nurse weighed 30 students in Year 10. Their weights (in kg) were recorded as follows:

50     52     53     54     55     65     60     70     48     63
74     40     46     59     68     44     47     56     49     58
63     66     68     61     57     58     62     52     56     58

a. Present this information in a frequency table.
b. Comment on the mode of the table.

Solution:

There are 7 class intervals. This is reasonable for the given data.

The frequency table is as follows:

We notice that the modal class interval is 55-59. That is, most of the students weigh between 55 and 59 kilograms.

Stemplots (Stem-and-leaf Plots)

A stemplot (stem-and-leaf plot) is a device used to group a small data set (up to about 50 data values). The data set is arranged in ascending order while retaining all the original data values. This enables us to find the first quartile, median and the third quartile readily. The stemplot is useful to obtain information about the centre, spread, shape and outliers of the distribution.

Constructing a Stemplot

In a stemplot, each data value is considered to have two parts, a stem and a leaf. The leading digit(s) of a data value form the stem, and the trailing digit(s) becomes the leaf.

Three examples of a stemplot follow:

Data values 65, 70 and 74 are recorded as shown below:

Data values 349, 366 and 480 are recorded as shown below:

Data values 35.8, 36.2 and 36.9 are recorded as shown below:

Note:

To construct a stemplot, we:

enter the stems to the left of a vertical dividing line and the leaf to the right of the vertical dividing line for each data value
record each data value as listed in the data set to construct an unordered stemplot.
Then we construct an ordered stemplot from the unordered version by arranging the leaves in ascending order.

Example 9

Prepare a stemplot for the following set of scores which are marks obtained by 16 students:

Solution:

A stemplot for the score values that range from 21 to 74 is as follows:

This stemplot is not ordered.

An ordered stemplot is obtained by arranging the leaves in order, as shown below.

Note:

For each value of the data, the stemis the tens digit and the leaf is the units digit.

Example 10

The following data represents the number of runs per innings a player has scored in a season.

Construct an ordered stemplot to display the data.

Solution:

An ordered stemplot for the scores that range from 4 to 127 is given below. Stems 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are formed by the tens digits; whereas, the stems 10, 11 and 12 are formed by the hundreds and tens digits. The leaves are formed by the unit digits of the values.

We notice that the scores 4, 116 and 127 are separated from the main body of the data. So, 4, 116 and 127 are outliers. The stemplot for the data consisting of outliers can be displayed as follows:

Note:

The value of 4 is listed at the top of the table as an outlier and the values of 116 and 127 are listed below the table as outliers.

Key Terms

tables, frequency tables, class intervals, stemplots, stem-and-leaf plots, stem, leaf

What is the size of the class interval?

The size, or width, of a class interval is the difference between the lower and upper class boundaries and is also referred to as the class width, class size, or class length.

When choosing a class interval you should have approximately how many intervals covering the entire range of data?

For most data, 6 to 15 classes are enough. Class intervals (lengths) should be equal. Intervals such as 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50, etc are desirable.

What is the midpoint for the 95 99 Score interval?

Real Limits	Apparent Limits	Midpoints
94.5-99.5	95-99	97
89.5-94.5	90-94	92
84.5-89.5	85-89	87
79.5-84.5	80-84	82

Lesson 2 Frequency Distribution - Behavioral Statistics in Actionwww2.palomar.edu › Stats › FrequencyDistributions › FreqDistributionsnull

What is the frequency distribution that shows frequencies for class intervals?

Histograms. A histogram is a graph in which class interval frequencies of continuous variables are represented by the areas of bars centred on the 'class interval' on the horizontal (x) axis.