Question

the table displays the scores of students on a recent exam. find the mean of the scores to the nearest 10th.

score | number of students
60 | 9
65 | 5
70 | 3
75 | 3
80 | 2
85 | 9
90 | 5
95 | 2

Explanation:

Step1: Calculate total score

Multiply each score by its number of students and sum them:
$60\times9 + 65\times5 + 70\times3 + 75\times3 + 80\times2 + 85\times9 + 90\times5 + 95\times2$
$= 540 + 325 + 210 + 225 + 160 + 765 + 450 + 190$
$= 540+325=865$; $865+210=1075$; $1075+225=1300$; $1300+160=1460$; $1460+765=2225$; $2225+450=2675$; $2675+190=2865$.

Step2: Calculate total students

Sum the number of students:
$9 + 5 + 3 + 3 + 2 + 9 + 5 + 2 = 9+5=14$; $14+3=17$; $17+3=20$; $20+2=22$; $22+9=31$; $31+5=36$; $36+2=38$.

Step3: Find the mean

Mean = $\frac{\text{Total Score}}{\text{Total Students}} = \frac{2865}{38} \approx 75.4$ (rounded to nearest tenth).

Answer:

75.4