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Here are a few recommended readings before getting started with this lesson.
Tadeo and Ramsha are foodies and love to explore the restaurants that pop up in their neighborhood. They have recorded data about the average price of the main dishes in each restaurant using a table of values.
Average Main Dish Price (Dollars) | ||||
---|---|---|---|---|
10.12 | 9.29 | 8.29 | 9.78 | 10.69 |
9.68 | 12.09 | 8.94 | 10.81 | 8.62 |
11.39 | 12.62 | 8.71 | 10.74 | 10.52 |
10.77 | 10.15 | 9.18 | 8.45 | 9.52 |
11.89 | 9.77 | 9.44 | 13.24 | 11.01 |
10.62 | 9.38 | 12.15 | 9.68 | 9.60 |
10.32 | 11.31 | 11.41 | 8.62 | 9.27 |
10.96 | 9.18 | 10.28 | 10.71 | 10.02 |
They would like to draw some conclusions from this data. However, they are not entirely sure how to proceed with this task. Find the following information to help these curious connoisseurs!
Tadeo and Ramsha are having fun learning about frequency distributions. Last weekend, two of the most exciting cricket games this season took place. Tadeo and Ramsha recorded the runs scored by the 22 players in each match. The data for Games 1 and 2 are shown in the table.
Game 1 | Game 2 | ||||||
---|---|---|---|---|---|---|---|
32 | 21 | 27 | 46 | 114 | 87 | 96 | 92 |
9 | 16 | 19 | 19 | 101 | 111 | 80 | 106 |
40 | 28 | 42 | 36 | 85 | 112 | 117 | 94 |
11 | 38 | 23 | 28 | 62 | 43 | 106 | 66 |
8 | 18 | 26 | 59 | 104 | 51 | 76 | 91 |
62 | 40 | 111 | 78 |
Cricket Runs Scored in Game 1 | |
---|---|
Number of Runs Scored | Frequency |
0−9 | 2 |
10−19 | 5 |
20−29 | 6 |
30−39 | 3 |
40−49 | 4 |
50−59 | 1 |
60−69 | 1 |
Number of Runs Scoredand the vertical axis the
Frequency.Then the bars will be drawn to represent the frequency of each interval.
Cricket Runs Scored in Game 2 | |
---|---|
Number of Runs Scored | Frequency |
40−49 | 1 |
50−59 | 1 |
60−69 | 2 |
70−79 | 2 |
80−89 | 3 |
90−99 | 4 |
100−109 | 4 |
110−119 | 5 |
There are special distributions that less common than skewed and symmetric distributions. These distributions may appear in situations such as an experiment where each event has the same probability or a sample taken from two separate populations. These are the uniform and bimodal distributions.
A box plot is another data display that allows one to see the shape of a frequency distribution. The length of the whiskers
and the position of the median tell whether the distribution is skewed or symmetric.
During their fantastic journey exploring the restaurants in their neighborhood, Tadeo and Ramsha found a fabulous Italian restaurant. While eating their food, they observed the people who entered the restaurant.
The two are curious about the average age of people eating at this restaurant. Therefore, they decide to collect data on the ages of people who enter the restaurant during a typical day.
Ages of People Who Enter the Italian Restaurant on a Typical Day | |||||
---|---|---|---|---|---|
15 | 53 | 55 | 60 | 38 | 56 |
62 | 14 | 44 | 24 | 32 | 10 |
42 | 54 | 47 | 67 | 60 | 50 |
61 | 30 | 30 | 62 | 62 | 65 |
56 | 52 | 35 | 25 | 34 | 32 |
They now want to draw some conclusions from this data set by displaying it in a box plot.
Five Number Summary | |
---|---|
Minimum Value | 10 |
First Quartile | 32 |
Median | 48.5 |
Third Quartile | 60 |
Maximum Value | 67 |
Now, draw a box from the first quartile to the third quartile. Then, draw a line through the median and the whiskers from the box to the minimum and maximum values.
Notice that this plot corresponds to option A.
Therefore, the option that states that 50% of the people who enter the Italian restaurant in a regular day are between 32 and 60 years old is the right one.
All the pieces to analyzing data using histograms have been covered. This method of displaying data makes it easier to find the data distribution and determine the best measures of center and variation to describe the data set. Recall the data Tadeo and Ramsha recorded about the main dishes of the restaurants in their neighborhood at the beginning of the lesson.
Average Main Dish Price (Dollars) | ||||
---|---|---|---|---|
10.12 | 9.29 | 8.29 | 9.78 | 10.69 |
9.68 | 12.09 | 8.94 | 10.81 | 8.62 |
11.39 | 12.62 | 8.71 | 10.74 | 10.52 |
10.77 | 10.15 | 9.18 | 8.45 | 9.52 |
11.89 | 9.77 | 9.44 | 13.24 | 11.01 |
10.62 | 9.38 | 12.15 | 9.68 | 9.60 |
10.32 | 11.31 | 11.41 | 8.62 | 9.27 |
10.96 | 9.18 | 10.28 | 10.71 | 10.02 |
The two students wanted to draw some insights and conclusions based on this data. However, they were not entirely sure how to proceed with this task. Find the following information to help these curious connoisseurs!
Average Main Dish Price (Dollars) | |
---|---|
Price Range | Frequency |
8.00−8.99 | 6 |
9.00−9.99 | 12 |
10.00−10.99 | 13 |
11.00−11.99 | 5 |
12.00−12.99 | 3 |
13.00−13.99 | 1 |
Price Rangeand the vertical axis the
Frequency.Then, draw the bars to represent the frequency of each interval.
Distribution | Measure of Center | Measure of Variation |
---|---|---|
Symmetric | Mean | Standard deviation |
Skewed | Median | Five-number summary |
Because in this situation the distribution of the data is skewed, the median and the five-number summary best describe the center and variation of the data, respectively.