Data Representation and Interpretation Alıştırma Soruları — ACT — Sayfa 2

Soru 21Soru →

A team of oceanographers monitored sea surface temperatures (SST, in ${}^\circ\text{C}$ ) at three distinct coral reef monitoring stations ( $S_1$ , $S_2$ , and $S_3$ ) during a 4-month summer observation period.

Table 1:

Station	June SST ( ${}^\circ\text{C}$ )	July SST ( ${}^\circ\text{C}$ )	August SST ( ${}^\circ\text{C}$ )	September SST ( ${}^\circ\text{C}$ )
$S_1$	27.5	28.5	29.5	28.5
$S_2$	28.0	29.0	30.0	31.0
$S_3$	26.5	27.0	28.5	28.0

Based on Table 1, what is the difference between the average 4-month SST at Station $S_2$ and the average 4-month SST at Station $S_3$ ?

2.0{}^\circ\text{C}

1.5{}^\circ\text{C}

1.0{}^\circ\text{C}

3.0{}^\circ\text{C}

Cevabı ve açıklamayı göster

Cevap: $2.0{}^\circ\text{C}$

Cevap

2.0{}^\circ\text{C}

To find the difference between the 4-month average SSTs at Station S₂ and Station S₃, first sum and average the monthly temperatures for each station. For Station S₂, the sum is 28.0 + 29.0 + 30.0 + 31.0 = 118.0 °C, and the average is 118.0 / 4 = 29.5 °C. For Station S₃, the sum is 26.5 + 27.0 + 28.5 + 28.0 = 110.0 °C, and the average is 110.0 / 4 = 27.5 °C. The difference between these two averages is 29.5 °C - 27.5 °C = 2.0 °C.

Adım Adım Çözüm

1

Calculate the 4-month average SST for Station

S_2

.

Sum =

28.0 + 29.0 + 30.0 + 31.0 = 118.0{}^\circ\text{C}

. Average =

118.0 / 4 = 29.5{}^\circ\text{C}

.

Finding the mean value requires summing all four monthly measurements for Station

S_2

and dividing by 4.

2

Calculate the 4-month average SST for Station

S_3

.

Sum =

26.5 + 27.0 + 28.5 + 28.0 = 110.0{}^\circ\text{C}

. Average =

110.0 / 4 = 27.5{}^\circ\text{C}

.

Finding the mean value requires summing all four monthly measurements for Station

S_3

and dividing by 4.

3

Subtract the average SST of Station

S_3

from the average SST of Station

S_2

.

29.5{}^\circ\text{C} - 27.5{}^\circ\text{C} = 2.0{}^\circ\text{C}

.

Determining the difference between the two calculated averages.

Anahtar Kavram

Calculating average values across multiple data points in a table and finding their numerical difference.

Soru 22Soru →

Plant physiologists measured the photosynthetic rate (in $\mu\text{mol CO}_2/\text{m}^2\cdot\text{s}$ ) of a C3 plant species exposed to three ambient temperature conditions ( $20^\circ\text{C}$ , $30^\circ\text{C}$ , and $40^\circ\text{C}$ ) under constant saturating light intensity. The measured photosynthetic rates were $15.0\ \mu\text{mol CO}_2/\text{m}^2\cdot\text{s}$ at $20^\circ\text{C}$ , $24.0\ \mu\text{mol CO}_2/\text{m}^2\cdot\text{s}$ at $30^\circ\text{C}$ , and $9.0\ \mu\text{mol CO}_2/\text{m}^2\cdot\text{s}$ at $40^\circ\text{C}$ .

Based on these data, is the following statement True or False?
"The mean photosynthetic rate of the plant across the three tested temperatures is $16.0\ \mu\text{mol CO}_2/\text{m}^2\cdot\text{s}$ ."

Doğru

Yanlış

Cevabı ve açıklamayı göster

Cevap: True

Cevap

True. The mean photosynthetic rate across all three tested temperatures is

16.0\ \mu\text{mol CO}_2/\text{m}^2\cdot\text{s}

.

The calculated average of the three photosynthetic rates (

15.0

,

24.0

, and

9.0

) is

\frac{15.0 + 24.0 + 9.0}{3} = \frac{48.0}{3} = 16.0\ \mu\text{mol CO}_2/\text{m}^2\cdot\text{s}

, which matches the claim directly.

Adım Adım Çözüm

1

Extract the photosynthetic rates for all three temperature conditions.

Rate at

20^\circ\text{C} = 15.0

, Rate at

30^\circ\text{C} = 24.0

, Rate at

40^\circ\text{C} = 9.0

.

Identifying all data points is required to calculate the overall average.

2

Sum the rates recorded across the three conditions.

15.0 + 24.0 + 9.0 = 48.0\ \mu\text{mol CO}_2/\text{m}^2\cdot\text{s}

.

Finding the total sum is the first step in calculating an arithmetic mean.

3

Divide the total sum by the total number of conditions (

n = 3

).

\frac{48.0}{3} = 16.0\ \mu\text{mol CO}_2/\text{m}^2\cdot\text{s}

.

Dividing the sum by the count yields the correct mean value.

Anahtar Kavram

Calculating Arithmetic Mean from Data Points

Soru 23Soru →

Biophysicists conducted an experiment measuring the action potential conduction velocity ( $v$ , in $\text{m/s}$ ) in unmyelinated giant nerve fibers as a function of fiber diameter ( $d$ , in $\mu\text{m}$ ) at a constant temperature of $20^\circ\text{C}$ . The recorded data is presented in Table 1.

Fiber Diameter ( $d$ , $\mu\text{m}$ )	Conduction Velocity ( $v$ , $\text{m/s}$ )
100	5.0
200	8.0
400	14.0
600	18.0
900	21.0

Based on Table 1, what is the average rate of change in conduction velocity, in $\text{m/s}$ per $100\,\mu\text{m}$ increase in fiber diameter, over the interval from $d = 200\,\mu\text{m}$ to $d = 600\,\mu\text{m}$ ?

Cevabı ve açıklamayı göster

Cevap: 2.5

Cevap

The average rate of change in conduction velocity over the specified interval is

2.5\,\text{m/s per }100\,\mu\text{m}

increase in fiber diameter.

To find the average rate of change in conduction velocity per

100\,\mu\text{m}

increase in fiber diameter between

d = 200\,\mu\text{m}

and

d = 600\,\mu\text{m}

, subtract the initial velocity (

8.0\,\text{m/s}

) from the final velocity (

18.0\,\text{m/s}

) to get

\Delta v = 10.0\,\text{m/s}

. Divide by the change in diameter

\Delta d = 600 - 200 = 400\,\mu\text{m}

to obtain

0.025\,\text{m/s per }\mu\text{m}

. Multiplying by

100

yields

2.5\,\text{m/s per }100\,\mu\text{m}

.

Adım Adım Çözüm

1

Locate data points for

d = 200\,\mu\text{m}

and

d = 600\,\mu\text{m}

in Table 1.

At

d = 200\,\mu\text{m}

,

v = 8.0\,\text{m/s}

. At

d = 600\,\mu\text{m}

,

v = 18.0\,\text{m/s}

.

These data points define the boundaries of the interval specified in the question.

2

Calculate the overall changes in velocity (

\Delta v

) and diameter (

\Delta d

).

\Delta v = 18.0 - 8.0 = 10.0\,\text{m/s}

and

\Delta d = 600 - 200 = 400\,\mu\text{m}

.

Calculating the rate of change requires dividing the change in the dependent variable by the change in the independent variable.

3

Scale the rate of change to a

100\,\mu\text{m}

diameter interval.

\frac{10.0\,\text{m/s}}{400\,\mu\text{m}} \times 100\,\mu\text{m} = 2.5\,\text{m/s per }100\,\mu\text{m}

.

The question asks specifically for the rate per

100\,\mu\text{m}

increase in diameter.

Anahtar Kavram

Calculating average rate of change and trend slopes from quantitative scientific data tables.

Data Representation and Interpretation

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