Question

There are 25 students in a class. The lowest quiz score is a 5. The average quiz score is 14, median is 15, and SD is 3. If the student who got a 5 has their grade changed to a 10, what happens to the average, the median, and the SD, respectively? Answer in detail.

Answer 1

1)changing one score from 5 to 10 , increases the total of the scores, and in turn, mean of the scores increases,

new mean =(previous total+change in value)/n =(25*5+(10-5))/25 =5.2

2) since median is the middle value and is higher than 10 . therefore median will not get affected by the change and remains same as 15

3)

since the lowest score comes closer to the mean average value , which in turn reduces the deviation from mean and therefore SD will decrease,

let previous distribution is X before change and after change it becomes Y.

from above x =25*14 =350

SS(x=n*(SD(x))²=x ²-(x)²/n =x ² -(350)²/25

25*3² =x ²-4900

x ²=4900+225 =5125

therefore new distribution:

y =x+(10-5) =350+5 =355

and y² = x²+(10²-5²) =5125+100-25 =5200

therefore new standard deviation SD(y) =sqrt((y²-(y)²/n)/(n) =sqrt((5200-355²/25)/25) =2.5219