Basic Statistical Calculations

2 questions

Question 1Question

Table 1 shows the heights of 5 sunflower seedlings grown under identical greenhouse conditions for 14 days.

SeedlingHeight (cm\text{cm})
Seedling 112
Seedling 215
Seedling 318
Seedling 415
Seedling 520

Based on the data in Table 1, match each statistical measure of seedling height to its correct calculated value.

Click a left item, then click its matching right item

Items

The mean height of the seedlings
The median height of the seedlings
The range of the seedling heights

Matches

Show answer & explanation

Answer

Mean corresponds to 16 cm16\text{ cm}, Median corresponds to 15 cm15\text{ cm}, and Range corresponds to 8 cm8\text{ cm}.
The mean height is the average value (16 cm16\text{ cm}), the median height is the middle value when the dataset is ordered (15 cm15\text{ cm}), and the range is the difference between the highest and lowest values (8 cm8\text{ cm}).

Step-by-Step Solution

1
Calculate the mean of the seedling heights.
16 cm16\text{ cm}
Sum the heights of all 5 seedlings (12+15+18+15+20=80 cm12 + 15 + 18 + 15 + 20 = 80\text{ cm}) and divide by the total number of seedlings (55) to obtain the arithmetic average: 805=16 cm\frac{80}{5} = 16\text{ cm}.
2
Determine the median of the seedling heights.
15 cm15\text{ cm}
Order the heights from least to greatest: 12,15,15,18,2012, 15, 15, 18, 20. The median is the middle value in this list, which is the third value (15 cm15\text{ cm}).
3
Calculate the range of the seedling heights.
8 cm8\text{ cm}
Identify the maximum height (20 cm20\text{ cm}) and the minimum height (12 cm12\text{ cm}). Subtract the minimum from the maximum to find the range: 2012=8 cm20 - 12 = 8\text{ cm}.

Key Concept

Basic Statistical Calculations
Question 2Question

An agricultural scientist measured the water absorption capacity of three different types of superabsorbent polymer gels (Gel A, Gel B, and Gel C) used in soil conditioning. Six trials were conducted for each gel type, and the mass of water absorbed (in grams per gram of gel) was recorded in the table below:

Gel TypeTrial 1 (g)Trial 2 (g)Trial 3 (g)Trial 4 (g)Trial 5 (g)Trial 6 (g)
Gel A42.144.541.843.245.042.6
Gel B51.548.253.449.850.652.1
Gel C33.735.234.032.936.134.5

Based on the table, what is the median water absorption capacity, in grams, for Gel B across the 6 trials?

Show answer & explanation

Answer: 51.05

Answer

The median water absorption capacity for Gel B across the 6 trials is 51.05 grams.
The correct answer is 51.05. To find the median value for Gel B, the 6 water absorption capacities must first be ordered from least to greatest: 48.2, 49.8, 50.6, 51.5, 52.1, and 53.4. Because there is an even number of values, the median is the average of the two middle values (50.6 and 51.5), which is 51.05.

Step-by-Step Solution

1
Identify the water absorption capacity values for Gel B.
51.5, 48.2, 53.4, 49.8, 50.6, and 52.1
To find the median, we must start with the complete set of data points for the specified group.
2
Sort the data points in ascending order.
48.2, 49.8, 50.6, 51.5, 52.1, 53.4
Calculating a median requires the values to be ordered from least to greatest.
3
Locate the middle values and calculate their average.
Middle values: 50.6 and 51.5. Average: 51.05
For an even number of data points, the median is the arithmetic mean of the two middle values.

Key Concept

Calculating the median of a dataset with an even number of values.
Basic Statistical Calculations Practice Questions — ACT | Examkin