Question

use the accompanying histogram to answer the following questions.

a) how many homes were included in the survey?
b) in how many homes were four televisions observed?
c) what is the modal class?
d) how many televisions were observed?
e) construct a frequency distribution from this histogram.

a) there were homes included in the survey.
(type a whole number.)

Explanation:

Read frequencies from the histogram

We first read the height of each bar in the histogram representing "Televisions per Home". The horizontal axis represents the number of televisions per home (from left to right: 1, 2, 3, 4, 5 televisions), and the vertical axis represents the "Number of Homes" (frequency):

• 1 television: 4 homes
• 2 televisions: 9 homes
• 3 televisions: 7 homes
• 4 televisions: 6 homes
• 5 televisions: 4 homes

Calculate total homes surveyed

To find the total number of homes included in the survey, we sum the frequencies of all classes:

$$ \text{Total Homes} = 4 + 9 + 7 + 6 + 4 = 30 $$

Determine homes with four televisions

From our reading of the histogram, the bar corresponding to 4 televisions has a height representing the number of homes:

$$ \text{Homes with 4 televisions} = 6 $$

Identify the modal class

Using the Modal Class concept, the modal class is the class with the highest frequency.
The highest frequency is 9, which corresponds to the class of homes with 2 televisions.

$$ \text{Modal Class} = 2 \text{ televisions} $$

Calculate total televisions observed

To find the total number of televisions observed, we multiply each number of televisions by its corresponding frequency (number of homes) and sum the products:

$$ \text{Total Televisions} = (1 \times 4) + (2 \times 9) + (3 \times 7) + (4 \times 6) + (5 \times 4) $$

$$ \text{Total Televisions} = 4 + 18 + 21 + 24 + 20 = 87 $$

Construct the frequency distribution

Using the Frequency Distribution concept, we organize the data into a table showing each class (Televisions per Home) and its corresponding frequency (Number of Homes):

• 1 television: 4 homes
• 2 televisions: 9 homes
• 3 televisions: 7 homes
• 4 televisions: 6 homes
• 5 televisions: 4 homes

Answer:

Question a

There were <blank>30</blank> homes included in the survey.

Question b

In <blank>6</blank> homes, four televisions were observed.

Question c

The modal class is <blank>2</blank> televisions.

Question d

There were <blank>87</blank> televisions observed.

Question e

The frequency distribution is:

Televisions	Frequency
2	9
3	7
4	6
5	4