A local library recorded the number of books read by students participating in a summer re… — ACT

A local library recorded the number of books read by students participating in a summer reading program. The results are summarized in the frequency table below.

Number of Books Read	Number of Students
$2$	$4$
$3$	$6$
$5$	$5$
$8$	$3$
$10$	$2$

What is the mean number of books read per student for this group?

$4.75$ Answer
B
$5.00$
C
$5.60$
D
$19.00$
E
$4.00$

Answer

The mean number of books read per student is

4.75

The value

4.75

is correct because finding the mean from a frequency table requires calculating the weighted sum of all data values divided by the total frequency. Multiplying each book count by its student count gives

2 \times 4 + 3 \times 6 + 5 \times 5 + 8 \times 3 + 10 \times 2 = 95

total books. Dividing

95

by the total student count of

20

yields

4.75

Step-by-Step Solution

Calculate the total number of students.

Total students =

4 + 6 + 5 + 3 + 2 = 20

To find the mean per student, the total number of participants is needed for the denominator.

Calculate the total number of books read by multiplying each value by its frequency and summing.

Total books =

(2 \times 4) + (3 \times 6) + (5 \times 5) + (8 \times 3) + (10 \times 2) = 8 + 18 + 25 + 24 + 20 = 95

The mean calculation requires the aggregate total of all books read across all students.

Divide the total number of books by the total number of students.

Mean =

\frac{95}{20} = 4.75

The mean of a frequency distribution is given by the total sum divided by the total frequency.

Key Concept

Weighted Mean from a Frequency Table

Estimated Time:1m 30s

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