StatisticsDescribing Data Using Tables and Graphs

Assignment 2Example Problems

Frequency Distributions

• Objective: Identify the class width, class midpoints, and class boundaries for the given frequency distribution

Daily Low Temperature

(°F)Frequency

50-53 154-57 358-61 562-65 1166-69 770-73 774-77 1

Frequency Distributions

• Class width is the difference between two consecutive lower class limits or two consecutive lower class boundaries and thus 53, 52, 51, 50 is a width of 4

Daily Low Temperature

(°F)Frequency

50-53 154-57 358-61 562-65 1166-69 770-73 774-77 1

Frequency Distributions

– Class midpoints are the values in the middle of the class. Because there is no “exact” middle we find by averaging the class width, that is (53-50)/2 = 1.5• So each lower value, add 1.5 to get the midpoints of

51.555.559.563.567.571.575.5

Daily Low Temperature

(°F)Frequency

50-53 154-57 358-61 562-65 1166-69 770-73 774-77 1

Frequency Distributions

– Class boundaries are the numbers used to separate the classes, but without the gaps created by the class limits• Find the center of the gaps and don’t forget about the lower

boundary49.553.557.561.565.569.573.577.5

Daily Low Temperature

(°F)Frequency

50-53 154-57 358-61 562-65 1166-69 770-73 774-77 1

Interpret Frequency Distributions

• Question: The data represents the daily rainfall (in inches) for one month. Construct a frequency distribution beginning with a lower class limit of 0.00 and use a class width of 0.20. Does the frequency distribution appear to be roughly a normal distribution?

0.35 0 0 0.21 0 0.510 0.24 0 0 1.34 0

0.19 0 0.02 0 0.23 00.18 0.56 0 0.02 0 0.23

0 0.17 0 0 0.11 0

Daily Rainfall (in inches)

Frequency

0.00-0.19 0.20-0.39 0.40-0.59 0.60-0.79 0.80-0.99 1.00-1.19 1.20-1.39

Interpret Frequency Distributions

• Answer: What I would do is put the data in numerical ascending order first. Because the frequency is the count and you want to “count” how many data items there are in the range 0.00-0.19. I have them highlighted below (but notice how much easier it would have been if they were sorted)

0.35 0 0 0.21 0 0.510 0.24 0 0 1.34 0

0.19 0 0.02 0 0.23 00.18 0.56 0 0.02 0 0.23

0 0.17 0 0 0.11 0

Daily Rainfall (in inches)

Frequency

0.00-0.19 220.20-0.39 0.40-0.59 0.60-0.79 0.80-0.99 1.00-1.19 1.20-1.39

Interpret Frequency Distributions

• Now continue to the 0.20-0.39

• I find 5 values in this range

0.35 0 0 0.21 0 0.510 0.24 0 0 1.34 0

0.19 0 0.02 0 0.23 00.18 0.56 0 0.02 0 0.23

0 0.17 0 0 0.11 0

Daily Rainfall (in inches)

Frequency

0.00-0.19 220.20-0.39 50.40-0.59 0.60-0.79 0.80-0.99 1.00-1.19 1.20-1.39

Interpret Frequency Distributions

• Then to 0.40-0.59

• I find two values. I also notice all that is left is 1.34 for I put this “one” in the last row

Daily Rainfall (in inches)

Frequency

0.00-0.19 220.20-0.39 50.40-0.59 20.60-0.79 00.80-0.99 01.00-1.19 01.20-1.39 1

0.35 0 0 0.21 0 0.510 0.24 0 0 1.34 0

0.19 0 0.02 0 0.23 00.18 0.56 0 0.02 0 0.23

0 0.17 0 0 0.11 0

Interpret Frequency Distributions

• For the second part of the problem:– Does the frequency distribution appear to be roughly

a normal distribution?• Answer: Remember graphically this would be a

bell curve. If I visually thought about 22 values in the tail end certainly this is not normal. Normal would have more in the middle and less in the ends. – In other words No, the distribution is not symmetric

and the frequencies do not start off low.

Graphing Frequency Distributions

• What if you wanted to actually see the graph of this data in your calculator?– First you need to enter the data in

your calculator• Press Stat / Edit and press Enter

Graphing Frequency Distributions

• You are now looking at a list where you can enter each value– Enter each value

from our example and press enter after each value entered 0.35 0 0 0.21 0 0.51

0 0.24 0 0 1.34 00.19 0 0.02 0 0.23 00.18 0.56 0 0.02 0 0.23

0 0.17 0 0 0.11 0

Graphing Frequency Distributions

• You are now looking at a list where you can enter each value– Enter each value

from our example and press enter after each value entered 0.35 0 0 0.21 0 0.51

0 0.24 0 0 1.34 00.19 0 0.02 0 0.23 00.18 0.56 0 0.02 0 0.23

0 0.17 0 0 0.11 0

Interpret Frequency Distributions

• Next we will set up the Histogram Window– Press Window• We saw from our frequency

distribution that our values are between 0 and 1.39. However, we want to have a little room to right and left– I set my Xmin = -0.5 and Xmax = 1.45

Daily Rainfall (in inches)

Frequency

0.00-0.19 220.20-0.39 50.40-0.59 20.60-0.79 00.80-0.99 01.00-1.19 01.20-1.39 1

Graphing Frequency Distributions

• The y values are the vertical direction and in our case the frequencies– These ranged from 0 to 22• Again make a little more room as I set

mine to -0.5 and 22.5 for the Ymin and Ymax

Daily Rainfall (in inches)

Frequency

0.00-0.19 220.20-0.39 50.40-0.59 20.60-0.79 00.80-0.99 01.00-1.19 01.20-1.39 1

Graphing Frequency Distributions

• Next we will set the Stat Plot– Press 2nd and then Y= to get to

the Stat Plot• The first plot should be selected

so press ENTER

Graphing Frequency Distributions

• Turn the Stat Plot On by pressing enter– Down arrow and then to the right to select

histogram and press enter– The Xlist: L1 is where the data is located• Remember you typed this in the list 1 column

• Press Graph

Daily Rainfall (in inches)

Frequency

0.00-0.19 220.20-0.39 50.40-0.59 20.60-0.79 00.80-0.99 01.00-1.19 01.20-1.39 1