A software engineering team recorded the number of technical bugs resolved daily over a pe… — ACT

A software engineering team recorded the number of technical bugs resolved daily over a period of $20$ days. The results are summarized in the frequency table below:

Bugs Resolved	Number of Days (Frequency)
$1$	$4$
$2$	$6$
$3$	$5$
$4$	$3$
$5$	$2$

What is the positive difference between the mean and the median number of bugs resolved daily during this $20$ -day period?

A
$0.00$
$0.15$ Cevap
C
$0.35$
D
$0.50$
E
$0.65$

Cevap

The positive difference between the mean and median number of bugs resolved daily is

0.15

To find the mean, multiply each bug count by its frequency, sum the products (

53

), and divide by the total frequency (

20

), yielding a mean of

2.65

. To find the median for

20

data points, locate the average of the

10\text{th}

and

11\text{th}

values in the cumulative frequency distribution. The

10\text{th}

value is

2

and the

11\text{th}

value is

3

, making the median

(2+3)/2 = 2.5

. The positive difference between the mean and median is

2.65 - 2.5 = 0.15

Adım Adım Çözüm

Calculate the total number of bugs resolved across all 20 days (the sum of products of values and frequencies).

\text{Total Bugs} = (1 \times 4) + (2 \times 6) + (3 \times 5) + (4 \times 3) + (5 \times 2) = 4 + 12 + 15 + 12 + 10 = 53

To find the mean of a frequency distribution, multiply each data value by its frequency and sum the results.

Calculate the mean number of bugs resolved per day.

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

Divide the total sum of bugs resolved by the total number of days (

20

Find the median of the ordered dataset of 20 values.

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

For

n = 20

data points, the median is the average of the

10\text{th}

and

11\text{th}

values in order. Looking at cumulative frequencies:

4

values are

1

, the next

6

values (positions

5

through

10

) are

2

, and the next

5

values (positions

11

through

15

) are

3

. The

10\text{th}

value is

2

and the

11\text{th}

value is

3

Compute the positive difference between the mean and the median.

\text{Difference} = |2.65 - 2.50| = 0.15

Subtract the median (

2.50

) from the mean (

2.65

Anahtar Kavram

Descriptive Statistics and Data Representations

Tahmini Süre:1m 15s

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Cevap

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