Gather a set of data. Choose a small sample, between 10 and 20 pieces of data, and a simple value to measure, such as the ages of visitors in a park, or the number of text messages each person in your family receives in one day.
Choose a display for your data, such as a frequency table, line plot, histogram, or bar graph. Display your data in your chosen format in a way that is misleading. You may use inconsistent (unequal) intervals, an uneven scale, and so on.
Use your display to draw a misleading inference about the data.
Display your data in the same format, this time making sure that it is not misleading.
Use this display to explain how your first display was misleading.
Use a data measure, such as mean, median, mode, or range, to draw a misleading inference about your data. Explain why the measure is misleading.
Im going to do a bar graph. I don't get the data thing...
The data is the raw numbers. You could ask 15 people in a park their ages. Your data is the 15 ages.
To gather a set of data, let's consider the number of hours people spend on social media each day. We will collect data from 15 individuals and record their daily social media usage in hours. The data set is as follows:
6, 4, 5, 7, 5, 6, 3, 5, 7, 8, 6, 4, 9, 5, 6
Now, I will choose a display format for the data. Let's go with a bar graph. In a misleading manner, I will manipulate the scale of the y-axis to misrepresent the frequencies. Here is a misleading bar graph:
```
Frequency
9 |
8 |
7 |
6 | *
5 | * *
4 | *
3 |
---------------
1 2 3 4 5
```
In this misleading graph, the y-axis scale is uneven, and the difference in frequency is exaggerated, making it appear as if there is significant variation in the data.
Now, let's display the data in a non-misleading format. Here is the accurate bar graph representation:
```
Frequency
9 | *
8 |
7 |
6 | ** *
5 | *** **
4 | ** *
3 | *
---------------
1 2 3 4 5
```
In this non-misleading graph, we can see a more accurate representation of the frequencies. The y-axis scale is consistent, and the variations in data are apparent but not exaggerated.
Now, let's use a measure like the mean to draw a misleading inference about the data. The mean is the sum of all values divided by the total number of values. In this case, the mean social media usage hours is given by:
Mean = (6+4+5+7+5+6+3+5+7+8+6+4+9+5+6) / 15 = 88 / 15 = 5.87
A misleading inference based on the mean could be that the majority of individuals spend close to 6 hours on social media each day.
However, this measure is misleading because it disregards the fact that there are extreme values in the data, such as 9 hours. Since the mean is influenced by extreme values, it may not accurately represent the typical social media usage. In this case, the mean overestimates the central tendency of the data due to the higher values, leading to a misleading inference.
To obtain a more representative measure, we can use the median. The median is the middle value when the data is arranged in increasing order. In this case, the median social media usage hours is 6.
The median is less influenced by extreme values, making it a more reliable measure for the central tendency of the data.