A local fitness center recorded the number of weekly workout sessions attended by a sample… — ACT

A local fitness center recorded the number of weekly workout sessions attended by a sample of $20$ members over the past month. The results are summarized in the frequency table below:

Sessions per Week	Number of Members
$1$	$4$
$2$	$6$
$3$	$5$
$4$	$3$
$5$	$2$

What is the positive difference between the mean and the median number of weekly workout sessions for these $20$ members?

$0.15$ Cevap
B
$0.35$
C
$0.50$
D
$0.65$
E
$8.10$

Cevap

The positive difference between the mean and median number of weekly workout sessions is

0.15

To find the mean, multiply each number of sessions by its frequency, sum the products, and divide by the total number of members (

20

(4 + 12 + 15 + 12 + 10) / 20 = 53 / 20 = 2.65

. To find the median for

20

members, take the average of the 10th and 11th values in order. Looking at cumulative frequencies, the 5th through 10th entries are

2

and the 11th through 15th entries are

3

. The median is

(2 + 3)/2 = 2.5

. The positive difference is

2.65 - 2.5 = 0.15

Adım Adım Çözüm

Calculate the total number of sessions.

(1 \times 4) + (2 \times 6) + (3 \times 5) + (4 \times 3) + (5 \times 2) = 4 + 12 + 15 + 12 + 10 = 53

Multiply each session value by its corresponding frequency to find the total sum of sessions.

Calculate the mean number of sessions.

\text{Mean} = \frac{53}{20} = 2.65

Divide the total number of sessions by the total number of members (

20

Find the median number of sessions.

\text{Median} = \frac{2 + 3}{2} = 2.5

With

20

total data points, the median is the average of the 10th and 11th ordered values. The cumulative frequencies show that the first

4

values are

1

, the next

6

values (5th through 10th) are

2

, and the next

5

values (11th through 15th) are

3

. The 10th value is

2

and the 11th value is

3

Calculate the positive difference between the mean and median.

|2.65 - 2.5| = 0.15

Subtract the median from the mean to find the difference.

Anahtar Kavram

Calculating mean and median from a frequency table

Tahmini Süre:1m 30s

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Cevap

Adım Adım Çözüm

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