How To Compare Two Sets Of Data
How to Compare Data Sets
Common graphical displays (e.g., dotplots, boxplots, stemplots, bar charts) can be effective tools for comparing data from two or more data sets.
4 Ways to Describe Information Sets
When you compare two or more data sets, focus on iv features:
- Unusual features. Unusual features refer to gaps (areas of the distribution where there are no observations) and outliers.
The residuum of this lesson shows how to use various graphs to compare data sets in terms of center, spread, shape, and unusual features. (This is a skill that students are expected to master for the Avant-garde Placement Statistics Test.)
Dotplots
When dotplots are used to compare data sets, they are positioned ane above the other, using the same scale of measurement, as shown below.
The dotplots show pet ownership in homes on two metropolis blocks. Here'south how to interpret the dotplots. Each dot represents a household. As shown in the plots, Cake A and Cake B both accept 15 dots. That means each cake has xv households. The numbers along the axis represent the number of pets owned past a household.
Pet buying is a picayune lower in Cake A. In Block A, most households have naught or one pet; in Block B, most households take two or more pets. In Block A, pet ownership is skewed right; in Block B, information technology is roughly bell-shaped. In Block B, pet ownership ranges from 0 to vi pets per household versus 0 to 4 pets in Block A; so there is more variability in the Block B distribution. At that place are no outliers or gaps in either information set.
Notation: You tin can count the number of pets in each block. Block A has v households with 0 pets, four households with 1 pet, 3 households with 2 pets, 2 households with 3 pets, and 1 household with 4 pets - 20 pets in all. Block B has 2 households with 0 pets, three households with 1 pet, 4 households with 2 pets, 3 households with 3 pets, 1 household with 4 pets, 1 household with 5 pets, and ane household with six pets - 35 pets in all. And so, Block B has more than pets than Cake A - even though both blocks have the aforementioned number of households.
Back-to-Back Stemplots
The back-to-dorsum stemplots are another graphic option for comparison data from two groups. The center of a back-to-back stemplot consists of a column of stems, with a vertical line on each side. Leaves representing one data set extend from the right, and leaves representing the other data set extend from the left.
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one
ane iv half-dozen
four 5 8
1 2 2 2 8 9
3 4 seven 9
2 5 eight
1 iii
0
1
two
3
iv
5
6
vii
1
two 6 eight
iii four 4 6 6 8 ix
four iii 6
4
The back-to-back stemplot higher up shows the amount of cash (in dollars) carried past a random sample of teenage boys and girls. The boys carried more greenbacks than the girls - a median of $42 for the boys versus $36 for the girls. Both distributions were roughly bong-shaped, although there was more variation among the boys. And finally, at that place were neither gaps nor outliers in either group.
Parallel Boxplots
With parallel boxplots (aka, side-by-side boxplots), information from two groups are displayed on the aforementioned chart, using the same measurement scale.
| Control group | ||||
| Treatment grouping | |||||||||||||||||||||
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The boxplot above summarizes results from a medical report. The handling grouping received an experimental drug to relieve common cold symptoms, and the command group received a placebo. The boxplot shows the number of days each grouping continued to study symptoms.
Neither boxplot reveals unusual features, such as gaps or outliers. Both plots are skewed to the right, although the skew is more prominent in the treatment grouping. The range of patient response was about the same in both groups. In the treatment grouping, cold symptoms lasted one to 15 days (range = xiv) versus three to 17 days (range = 14) for the command group. The median recovery time is more telling - about v days for the handling group versus about ix days for the command grouping. It appears that the drug may have had a positive effect on patient recovery.
Double Bar Charts
A double bar chart is similar to a regular bar chart, except that it provides two pieces of information for each category rather than just one. Oftentimes, the charts are color-coded with a different colored bar representing each piece of data.
The double bar nautical chart above shows customer satisfaction ratings for different cars, broken out by gender. The blue bars stand for males; the red confined, females.
Both groups prefer the Japanese cars to the American cars, with Honda receiving the highest ratings and Ford receiving the everyman ratings. Moreover, both genders agree on the rank order in which the cars are rated. As a group, the men seem to exist tougher raters; they gave lower ratings to each car than the women gave.
Examination Your Understanding
Problem
The back-to-back stemplot beneath shows the number of books read in a yr by a random sample of college and high school students.
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3 6 6
ane 2 3 four
6 viii viii 9
2 8
3
0
1
two
3
4
5
six
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Which of the post-obit statements are true?
I. Seven higher students did not read any books.
II. The college median is equal to the high schoolhouse median.
3. The mean is greater than the median in both groups.
(A) I only
(B) Two only
(C) 3 just
(D) I and II
(East) II and III
Solution
The correct reply is (Due east). None of the college students failed to read a volume during the yr; the fewest read was seven. In both groups, the median is equal to 24. And the mean number of books read per year is 25.3 for high school students versus 30.4 for college students; so the mean is greater than the median in both groups.
Source: https://stattrek.com/statistics/charts/compare-data-sets.aspx
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