A local bakery recorded the number of custom cakes sold per week over a 6-week period: 12,… — ACT

A local bakery recorded the number of custom cakes sold per week over a 6-week period: $12$ , $15$ , $8$ , $15$ , $14$ , and $10$ . If the bakery sells $x$ cakes in the 7th week such that the mean number of cakes sold per week for the entire 7-week period is $13$ , what is the median number of cakes sold over the 7-week period?

A
$12$
B
$13$
$14$ Cevap
D
$15$
E
$17$

Cevap

The median number of cakes sold over the 7-week period is

14

The total sales required for a 7-week average of

13

cakes is

7 \times 13 = 91

. Subtracting the sum of the first 6 weeks (

74

) gives

17

cakes for the 7th week. Arranging the 7 weekly values in order (

8, 10, 12, 14, 15, 15, 17

) shows that the 4th value, which is the median, is

14

Adım Adım Çözüm

Calculate the sum of the sales for the first 6 weeks.

12 + 15 + 8 + 15 + 14 + 10 = 74

To find the missing 7th week sales, we first need the total sales of the known weeks.

Determine the required total sales for a 7-week mean of 13.

7 \times 13 = 91

Mean is total sum divided by the number of data points, so Total = Mean

\times

Count.

Find the sales in the 7th week (

x

x = 91 - 74 = 17

Subtracting the 6-week sum from the 7-week total yields the 7th week value.

Order all 7 data points from least to greatest and identify the middle value.

Ordered list:

8, 10, 12, 14, 15, 15, 17

. The 4th item (median) is

14

The median of an odd number of data values is the middle value when arranged in ascending order.

Anahtar Kavram

Descriptive Statistics: Combining mean calculations to solve for missing data and finding the median of an ordered dataset.

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