Question

12. The heights of 53 students at Park School are shown in the histogram below.

Height of Students

18

Number of Students

NA ON

44 46 48 50 52 54 56 58 60

Height (inches)

Based on the data in the histogram, which statement is true?

A There are 12 students between 46 and 50 inches in height.

B. Exactly 18% of the students are between 52 and 54 inches in height.

C. More students are between 54 and 60 inches than between 46 and 50 inches in height.

Fewer students are between 44 and 52 inches than between 52 and 60 inches in height.

D

Answer 1

Fewer students are between 44 and 52 inches than between 52 and 60 inches in height.

Explanation:

Given

See attachment for histogram

Required

Select the true statement

Option A: Class 46-50 = 12 students

From the histogram, we have:'

`Class\ 46 - 48 = 8; Class\ 48 - 50 = 3`

So:

`Class\ 46 - 48 = Class\ 46 - 48 + Class\ 48 - 50`

`Class\ 46 - 48 = 8+ 3`

`Class\ 46 - 48 = 11`

(a) is false

Option B: %Class 52-54 = 18%

From the histogram, we have:'

`Class\ 52-54 = 18`

and

`Total = 53`

So, the percentage is:

`\% Class\ 52-54 = (Class\ 52-54)/(Total)`

`\% Class\ 52-54 = (18)/(53)`

`\% Class\ 52-54 = 0.3396`

Express as percentage:

`\% Class\ 52-54 = 33.96\%`

(b) is false

Option C: Class 54-60 > Class 46 - 50 students

From the histogram, we have:'

`Class\ 54-60 =Class\ 54-56 + Class\ 56-58 + Class\ 58-60`

`Class\ 54-60 = 4 + 4+3`

`Class\ 54-60 = 11`

In (a), we have:

`Class\ 46 - 48 = 11`

By comparison:

`Class\ 54-60 =Class\ 46 - 48 = 11`

(c) is false

Option D: Class 44-52 < Class 52 - 60 students

From the histogram, we have:'

`Class\ 44-52 =Class\ 44-56 + Class\ 46-48 + Class\ 48-50 +Class\ 50-52`

`Class\ 44-52 = 4+8+3+9`

`Class\ 44-52 = 24`

`Class\ 52-60 =Class\ 52 - 54 + Class\ 54-56 + Class\ 56-58 + Class\ 58-60`

`Class\ 52-60 = 18+ 4 + 4+3`

`Class\ 52-60 = 29`

By comparison:

`24 < 29`

i.e.

`Class\ 44 - 55 < Class\ 52 - 60`

(d) is true