Question

It’s a lazy Saturday afternoon, and you are excited to try out some of the quantitative data skills you’ve learned about in Biology 113. In particular, you want to know how big grasshoppers are. So you go out to the park, collect some grasshoppers and measure their length and weight.

Using the data shown in Table 2 below, calculate the descriptive statistics listed below for the lengths of the grasshoppers you measured.

Grasshopper          length               mass

1                                 20                   620

2                                 21.5                750

3                                 22                   800

4                                 23                   980

5                                 22                   960

6                                 25                   1100

1.what is Mean of the lengths:,Median: Mode: and Range:

2.Based on the descriptive statistics you have just calculated, what can you say about the distribution of grasshopper lengths in this sample? Consider both central tendency and dispersion.

3.As more data points (and more grasshoppers) are added to your collection, what can you say about the distribution of measurements and the mean length of the overall population?

4.Looking at the length and mass (weight) data, you’re starting to wonder whether there is a direct relationship between the length and mass of these grasshoppers.

What would the null hypothesis be for this test?

5.What type of graph or plot would you use to show this data and the results of the statistical test?

Answer 1

1) Mean = (20+21.5+22+23+22+25)/6 = 22.25 cm

Median is the middle value after arranging in ascending or descending order

= Middle value of (20, 21.5, 22, 22, 23, 25)

= (22 +22)/2

= 44/2

= 22

Mode is the most repeated value. Here mode is 22 as it is repeated twice.

Range is maximum value minus minimum value,

= 25 - 20

= 5

2) The mean length of grass hoppers is 22.25 cm, median and mode are 22 cm and range is 5. Based on this data, we can assume that the length of grasshoppers hovers around the mean (22.25 cm) and ranges between 20 and 25 cm. The distribution is normal.

3) As more data points are added, the normal distribution curve will become more smooth and the mean length of overall population is at the center of distribution curve.

4) Null hypothesis would be there is no association between the length and mass of grasshoppers.

5) Scatter plot is used to show the relation between these two variables. Test of correlation (Pearson correlation) is used to find the association between these two quantitative variables.