Question

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Daisy measured the heights of 20 plants.
The table gives some information about the heights (h in cm) of the plants.
Height of plants (h) Frequency
0< < 10
10 <n< 20
4
20 <h<30
30 <h <40
2
40 <h <50
50 <h < 60
3
|
By using the midpoints of each group, work out an estimate
for the mean height of a plant.
Will will
be
acer​

Answer 1

Answer:

33.25 cm

Step-by-step explanation:

Some of the information are missing in the table. We complete it as follows:

Height of plants (h) Frequency

0<h< 10   2

10 <h< 20  4

20 <h<30  5

30 <h <40  2

40 <h <50  4

50 <h < 60  3

In order to find an estimate for the mean height of a plant, we start by evaluating the midpoint of each class; the midpoint is just calculated as

$x=\frac{b-a}{2}$

where b is the maximum value of the group and a is the minimum value.

For instance, for the first group,

$x_1=\frac{10-0}{2}=5$

Therefore, the midpoints of the other groups are:

$x_2=15\\x_3 = 25\\x_4 = 35\\x_5 = 45\\x_6 = 55$

The mean height of the plant can be calculated using the formula:

$\bar h = \frac{\sum x_i f_i}{\sum f_i}$

where $f_i$ are the frequencies of each group, and where $\sum f_i$ is the sum of the frequencies.

We have

$\sum f_i = 20$

Therefore:

$\bar h = \frac{5\cdot 2 + 15\cdot 4 + 25\cdot 5 + 35\cdot 2 +45\cdot 4 + 55\cdot 4}{20}=33.25 cm$

Answer 2

The mean point of the each group can be calculated using midpoint and mean formula. The mean is sum of all the term divided by number of term.

The mean height of a plant is 30.5.

Given:

The height of plant and frequency is given in table.

Refer the attached table for the calculation of mid point and frequency of midpoint.

Now we have ,

$\rm {Sum \:of\: frequencies} = 20$

${\rm Sum \:of\: frequency\: \times midpoint\: product} = 610$

Calculate the mean of height of a plant.

$\rm Mean=\dfrac{610}{20}\\\rm Mean=30.5$

Thus, the mean height of a plant is 30.5.

Learn more about mean here:

https://brainly.com/question/17711864