A biology class recorded the height, in centimeters, of 15 plant seedlings after two weeks… — ACT

A biology class recorded the height, in centimeters, of $15$ plant seedlings after two weeks of growth. The frequency table below summarizes the recorded measurements:

Height (cm)	Number of Seedlings
$3$	$2$
$4$	$4$
$5$	$5$
$6$	$3$
$7$	$1$

What is the positive difference between the mean height and the median height, in centimeters, of these $15$ seedlings?

A
$0.0$
$0.2$ Cevap
C
$0.5$
D
$0.8$
E
$1.2$

Cevap

The positive difference between the mean height and the median height is

0.2

centimeters.

To calculate the mean height, multiply each height by its frequency, sum the products (

72

), and divide by the total number of seedlings (

15

), giving

4.8

cm. To find the median, locate the middle value (

8^{\text{th}}

value) in the ordered dataset of

15

measurements, which is

5.0

cm. The positive difference between

5.0

cm and

4.8

cm is

0.2

cm.

Adım Adım Çözüm

Calculate the total sum of all seedling heights using the frequency table

(3 \times 2) + (4 \times 4) + (5 \times 5) + (6 \times 3) + (7 \times 1) = 6 + 16 + 25 + 18 + 7 = 72

Each height value must be multiplied by its corresponding frequency count to find the total sum.

Calculate the weighted mean height

Mean =

\frac{72}{15} = 4.8

The sum of all heights (

72

) is divided by the total number of seedlings (

15

Determine the median height of the

15

seedlings

Median =

5.0

For

15

ordered values, the median is the

8^{\text{th}}

data point. Accumulating counts from smallest height:

2

(at height 3)

+ 4

(at height 4)

= 6

values. The next

5

values (positions 7 through 11) all have a height of 5. Therefore, the

8^{\text{th}}

value is

5.0

cm.

Find the positive difference between the mean and the median

|4.8 - 5.0| = 0.2

Subtracting the mean (

4.8

) from the median (

5.0

) gives a positive difference of

0.2

cm.

Anahtar Kavram

Descriptive Statistics and Data Representations

Tahmini Süre:1m 30s

Soru

Cevap

Adım Adım Çözüm

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