Question

the midterm scores on a biology exam for 30 students are listed below. 82, 45, 37, 94, 98, 74, 87, 89, 63, 76, 27, 86, 69, 98, 39, 75, 61, 43, 99, 86, 92, 65, 80, 82, 75, 91, 53, 90, 68, 98 (a) find the mean (average) score. (round to 2 decimal places.) answer: (b) find the median score. answer: (c) find the mode. answer: (d) suppose every student received 2 extra point on the exam. i. what would the new mean be? answer: ii. what would the new median be? answer: iii. what would the new mode be? answer:

Explanation:

Step1: Calculate sum of scores

Sum all 30 scores: $82 + 45+37 + 94+98+74+87+89+63+76+27+86+69+98+39+75+61+43+99+86+92+65+80+82+75+91+53+90+68+98=2190$

Step2: Calculate mean

Use formula $\text{Mean}=\frac{\text{Sum of data}}{\text{Number of data}}$. Here, number of data $n = 30$. So, $\text{Mean}=\frac{2190}{30}=73.00$

Step3: Find median

Arrange scores in ascending order: $27,37,39,43,45,53,61,63,65,68,69,74,75,75,76,80,82,82,86,86,87,89,90,91,92,94,98,98,98,99$. Since $n = 30$ (even), median is average of $\frac{n}{2}=15$ - th and $(\frac{n}{2}+1)=16$ - th ordered values. Median $=\frac{76 + 80}{2}=78$

Step4: Find mode

The mode is the most - frequently occurring value. Here, 98 appears 4 times, more frequently than any other value, so mode is 98.

Step5: Calculate new mean, median and mode when 2 is added to each score

If 2 is added to each score:

• New mean: $\text{New Mean}=\text{Old Mean}+2=73 + 2=75.00$
• New median: $\text{New Median}=\text{Old Median}+2=78+2 = 80$
• New mode: $\text{New Mode}=\text{Old Mode}+2=98 + 2=100$

Answer:

(a) 73.00
(b) 78
(c) 98
(d)
i. 75.00
ii. 80
iii. 100