A community center hosted 5 different skill workshops on a Saturday. The table below shows… — ACT

A community center hosted 5 different skill workshops on a Saturday. The table below shows the number of participants in each workshop and the mean satisfaction rating (on a scale from 1 to 10) reported by the participants in that workshop.

Workshop	Number of Participants	Mean Satisfaction Rating
Pottery Basics	12	8.0
Creative Writing	8	9.0
Photography	15	7.0
Graphic Design	10	8.5
Woodworking	5	10.0

What is the overall weighted mean satisfaction rating for all $50$ participants combined across all five workshops?

$8.16$ Cevap
B
$8.50$
C
$7.00$
D
$8.00$
E
$7.96$

Cevap

The overall weighted mean satisfaction rating for all 50 participants is 8.16.

The correct answer is obtained by calculating the weighted mean. Multiplying each workshop's rating by its number of participants gives the total points contributed by that group. Adding these products gives a total of 408 satisfaction points across all 50 participants. Dividing 408 by 50 yields an overall weighted average of 8.16.

Adım Adım Çözüm

Calculate the total sum of satisfaction ratings for each workshop

Pottery:

12 \times 8.0 = 96

; Creative Writing:

8 \times 9.0 = 72

; Photography:

15 \times 7.0 = 105

; Graphic Design:

10 \times 8.5 = 85

; Woodworking:

5 \times 10.0 = 50

Each participant's rating contributes to the total sum for their workshop.

Sum the total satisfaction points across all workshops

96 + 72 + 105 + 85 + 50 = 408

This gives the total combined satisfaction points for all participants.

Divide the total combined satisfaction points by the total number of participants

\frac{408}{50} = 8.16

The weighted mean requires dividing the overall sum of scores by the total sample size (

50

participants).

Anahtar Kavram

Weighted Mean from Summary Data Tables

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