Data loss and recovery

Activity: What do Ladybugs Look Like? 

Fun Facts:-

• Their name is Legendry - Legend has it that the “lady” in lady beetle dates back to the Middle Ages. The story is that farmers' crops were being damaged by swarms of aphids. But after the farmers prayed to the Virgin Mary for help, the ladybugs arrived, ate all the aphids, and saved the day. The farmers were so grateful that from then on they referred to the insects as “Our Lady’s beetles.”

• They went to space! - In 1999, four appropriately named ladybugs, John, Paul, Ringo, and George (after The Beatles of course) went to space! The four lucky bugs were brought to space, along with their favourite snack, aphids, so that scientists could observe how the predators and their prey would interact in zero gravity.  

• Ladybugs chew, but not in the way you might think - That’s right, ladybugs chew their food! But unlike you and I who chew up and down, ladybugs chew by moving their jaws side to side.

• Bonus Fact! - The wings of a ladybug beat 85 times per second when they fly! Crazy eh? 

Activity: What do Ladybugs Look Like? 

In this activity, we will collect, summarize, and compare data on what do ladybugs look like. We will formulate three statistical investigative questions: 

1. What do ladybugs usually look like? 
2. How many spots do ladybugs typically have? 
3. Do red ladybugs tend to have more spots than black ladybugs? 

Collect data 

You will be provided with secondary data in the form of a picture of ladybugs (See Fig 1.1). As you see the pictures, you will notice a variation in the number of spots on the ladybugs and their color. You can now record information about the number of spots, the color of each ladybug pictured, or any other features you think might be relevant. 

You need to create some data collection questions that will need to be answered for each ladybug, to begin with, the statistical investigative questions: 

How many spots are on the ladybug?

What color is the ladybug? 

What color are the spots on the ladybug? 

The number of spots on a ladybug is an example of numerical variables from taking measurements or counting objects. Numerical variables are also called quantitative variables. The color of the ladybug is an example of a categorical variable. Data on categorical variables are observed according to their category, where the categories are mutually exclusive and jointly exhaustive, meaning they do not overlap and represent all possible observations.

Now you can select the categories to use for color: black, orange, and red. 

For each of the photos, you will ask the data collection questions and record the information for the three variables: (1) color of the body, (2) number of spots, and (3) the color of the spots (if applicable). You should note that ladybugs are symmetrical, so if you count the spots on one side, you know the number on the other side. The total number of spots is recorded. 

                                                                Fig 1.1 - 4x4 photo card of ladybug

Sometimes data are messy or not straightforward. For instance, some of the spots are very faded and do not look like a spot at all. It is essential you and your class decide what will count as a spot (e.g., whether all shaped markings and all spots along the margin of the hard wing case will be counted). These consensus discussions will help reduce the measurement error introduced by your classmate's recording information on the ladybugs you are viewing. You should understand the importance of collecting data consistently. 

You might record the data you are collecting in a variety of ways. You could consider one variable and record the values for each ladybug as in the below table.

You might record all three variables at once. For example, you might record the answer to all three questions for each ladybug as in the below table.

Table of ladybugs data card

This shows an example of a possible table structure showing from left to right in the cell: number of spots, the color of the body (R or B or O), the color of spots (B or R or O). Each of the cells can be thought of as a data card, an organizational tool for data. You can begin to recognize the importance of having a strategy that allows you to organize the data in a useful way. Eventually, it would be best if you were looking to create a more productive way to organize the data. It would help if you created a data table where each observation is on a separate row. This could be done on a worksheet using paper and pencil or using technology. 

Data table for ladybug card

Analyze the data 

You could use a picture graph to analyze the data. This allows you to keep track of which ladybug is being graphed. Now you can use another graphical representation for one quantitative variable, which is a dot plot. You should be able to match a ladybug to a dot on the plot. This is a meaningful connection, as a dot plot no longer allows an individual ladybug to be distinguished. Dot plots can be created by hand or using technology, and the horizontal axis typically represents the values of the variable under study. 

To compare the number of spots on ladybugs of different colors, you might use multiple dot plots with the same scale stacked one on top of the other. See the next figure as an example. 

Using either a single dot plot or multiple dot plots broken down by ladybugs' different colors, you can answer a series of analysis questions about the quantitative variable number of spots.

                                          Fig - Drawn stacked dot plots on spot count for different color ladybugs
    

For example, such questions might include: 

What number of spots were most common/ typical for all the ladybugs? Red ladybugs only? Orange ladybugs? Black ladybugs? 

What is the least/greatest number of spots for the ladybugs? Red ladybugs only? Orange ladybugs? Black ladybugs? 

It would help if you thought about distributing a quantitative variable and the variability in the values. You should understand that the median represents the value at the middle or center of a quantitative variable's distribution. A median has the same number of data points (approximately half) are greater than and are less than it. The medians in figure 1.12 are 12 spots for the red ladybugs, 14 for the orange, and 2 spots for the black.

Interpret the data 

Using the analyses, you can answer the statistical investigative question "What do ladybugs usually look like?" with an answer that might include the following: 

Based on the pictures, the ladybugs in the card set were a mixture of red, orange, and black ladybugs. The red ladybugs had between 0 and 18 black spots. The orange ladybugs had between 10 and 20 black spots. The black ladybugs were different because they had either 2 or 4 spots in a mixture of colors. Some of your classmates may write the following to answer the question, "How many spots do ladybugs in our card set have?": 

Red ladybugs have between 0 and 18 spots. The most common number of spots is 16. The median number of spots for red ladybugs is 12 spots. 

Orange ladybugs have between 10 and 20 spots. The median number of spots for orange ladybugs is 14 spots. 

This is a bit higher than the red ladybugs. Black ladybugs have two or four spots. Out of the three ladybugs, two had 2 spots, and one had 4 spots. 

To answer the comparative question, "Do red ladybugs tend to have more spots than black ladybugs?" you may answer: 

Red ladybugs have between 0 and 18 spots. The most common number of spots is 16. The median number of spots for red ladybugs is 14 spots. Black ladybugs only have 2 or 4 spots. 

The median of spots for black ladybugs is 2. There is only one red ladybug with less than 6 spots; there is one with zero spots. All other red ladybugs have 6 or greater spots.

 These analyses suggest that black ladybugs in our pictures tend to have fewer spots than red ladybugs.