# MATH 1530 Lecture Notes - Lecture 2: Line Segment, Becquerel, Simple Random Sample

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MATH 1530: Elementary Probability and Statistics Name: ______________________________

Chap 2: Summarizing and Graphing Data – Class Activity Worksheet

Frequency Distribution (or Frequency Table) shows how a data set is partitioned among all of

several categories (or classes) by listing all of the categories along with the number of data values in each of the

categories. The frequency for a particular class is the number of original values that fall into that class.

Class Width is the difference between two consecutive lower class limits or two consecutive

lower class boundaries.

Lower Class Limits are the smallest numbers that can actually belong to different classes.

Upper Class Limits are the largest numbers that can actually belong to different classes.

Class Boundaries are the numbers used to separate classes and can be found by adding the upper class limit to

the lower class limit OF CONSECUTIVE CLASSES and dividing the sum by two.

Class Midpoints are the values in the middle of the classes and can be found by adding the lower class limit to

the upper class limit OF THE SAME CLASS and dividing the sum by two.

Outliers: Sample values that lie very far away from the vast majority of other sample values.

Relative Frequency Distribution (or Relative Frequency Table) includes the same class limits as a frequency

distribution, but the frequency of a class is replaced with a relative frequencies (a proportion) or a percentage

frequency ( a percent).

Relative frequency 100%

class frequency

sum of all frequency

Note: The sum of the relative frequencies in a relative frequency distribution MUST be close to 100%.

Cumulative Frequency Distribution (or Cumulative Frequency Table). The cumulative frequency for a class is

the sum of the frequencies for that class and all previous classes.

Normal distribution: Distribution with the characteristic that it has a “bell” shape. i.e. The frequencies start low,

then increase to one or two high frequencies, then decrease to a low frequency (The distribution is

approximately symmetric, with frequencies preceding the maximum being roughly a mirror image of those that

follow the maximum).

Histogram: A graph consisting of bars of equal width drawn adjacent to each other (without gaps). The

horizontal scale represents the classes of quantitative data values and the vertical scale represents the

frequencies.

The heights of the bars correspond to the frequency values.

The bars on the horizontal scale are labeled with one of the following: Class boundaries OR Class

midpoints.

A distribution of data is skewed if it is not symmetric and extends more to one side or the other.

Data skewed to the right (positively skewed) have a longer right tail.

Data skewed to the left (negative skewed) have a longer left tail.

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STATITICL GRAPHS

Frequency Polygon: A line graph that uses line segments connected to points (frequency of each class) directly

above class midpoint values.

Ogive: A line graph that depicts cumulative frequencies. An ogive uses class boundaries along the horizontal

scale, and cumulative frequencies along the vertical scale.

DotPlot: Consists of a graph in which each data value is plotted as a point (or dot) along a scale of values. Dots

representing equal values are stacked.

Stemplot (or Stem-and-Leaf Plot): Represents quantitative data by separating each value into two parts: the

stem (such as the leftmost digit (s)) and the leaf (such as the rightmost digit).

1. The accompanying table below represents a frequency distribution for the FICO credit rating scores of a

sample of size 100. Use the table to find the requested:

a) What is the class width for this frequency distribution? _______________________

b) Complete the table by finding the class boundaries, the class mid-points, the relative frequencies

(percentage), and the cumulative frequencies of all the classes.

Class

Boundaries

FICO Score

classes

Class

Mid-point

Frequency

Relative

Frequency

Cumulative

frequency

400 – 449

1

450 – 499

1

500 – 549

5

550 – 599

8

600 – 649

12

650 – 699

16

700 – 749

19

750 – 799

27

800 – 849

10

850 - 899

1

c) Are there any possible outliers in the data? _____________________

d) Among those sampled, how many FICO score are greater or equal to 750? ___________________

e) Among those sampled, how many FICO scores are less than 650? ___________________________

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f) Draw a Histogram representing the data set. Use Class boundaries on the horizontal axis (starting with

the first class boundary at origin) and frequencies on the vertical axis (starting at zero). Label your axis.

g) Is the shape of the distribution of the data normal (bell-shaped) or skewed? __________________

h) Draw a Frequency Polygon representing the data set. Use Class midpoints on the horizontal axis (starting

with the first class midpoint at the first scaling from the origin) and frequencies on the vertical axis

(starting at zero). Label your axis. Note: The Line segment starts at the origin (0,0).