A classroom of students has their heights measured (in inches) for statistics investigation. The tallest student in the class is 71 inches tall. One student is assigned to record all the values. That student made a mistake when recording one of the values. When they meant to record the 71, they accidentally entered 711.How will the mean and SD be affected by this mistake?a. The mean and SD will be unaffected by the mistake.b. The mean and SD will be decreased by the mistake.c. The mean and SD will be increased by the mistake.

We are given that a classroom of students has their heights measured (in inches) for statistics investigation. The tallest student in the class is 71 inches tall. That student made a mistake when recording one of the values. When they meant to record the 71, they accidentally entered 711.

Now, we have to assess the impact of this mistake on Mean and SD.

Firstly, Mean will increase due to this mistake as Mean formula is given by;

Mean = (sum of all values) ÷ Total no. of observations

Since, the number mistakenly recorded as 711 which is higher than 71 so due to this numerator will increase and because of which the mean will also increase by the mistake.

Secondly, Standard deviation will also increase due to this mistake as SD formula is given by;

SD = [tex]\frac{\sum (X-Xbar)^{2} }{n-1}[/tex]

Here, in the numerator it can be seen that each data value is subtracted from the mean value and then it is being squared so due to increase in one number of 711 the one data value square becomes large and due to which numerator sum will increase and hence, SD will also increase by this mistake.