For an upcoming government project, you are required to find the average height of the students in Class VIII of a given school. Instead of asking every student, you took a few students as your sample and noted their heights in the table given below. Roll Number Height8012 121.92 cm8045 133.21 cm8053 141.34 cm8099 126.23 cm8125 175.74 cmQuestion 3/3MandatorySamplingWhat is the standard deviation of the sample?22.8423.6719.1921.45

To calculate the standard deviation of the sample, we first need to find the mean (average) of the heights.

Step 1: Calculate the mean (average) Add up all the heights and divide by the number of students.

121.92 cm + 133.21 cm + 141.34 cm + 126.23 cm + 175.74 cm = 698.44 cm

698.44 cm / 5 students = 139.688 cm (This is the mean height)

Step 2: Subtract the mean from each height (deviation) Now, subtract the mean from each height to get the deviation for each.

121.92 cm - 139.688 cm = -17.768 cm 133.21 cm - 139.688 cm = -6.478 cm 141.34 cm - 139.688 cm = 1.652 cm 126.23 cm - 139.688 cm = -13.458 cm 175.74 cm - 139.688 cm = 36.052 cm

Step 3: Square each deviation Next, square each deviation.

(-17.768 cm)^2 = 315.77 cm^2 (-6.478 cm)^2 = 41.97 cm^2 (1.652 cm)^2 = 2.73 cm^2 (-13.458 cm)^2 = 181.08 cm^2 (36.052 cm)^2 = 1299.74 cm^2

Step 4: Calculate the mean of these squared deviations Add up all the squared deviations and divide by the number of students.

315.77 cm^2 + 41.97 cm^2 + 2.73 cm^2 + 181.08 cm^2 + 1299.74 cm^2 = 1841.29 cm^2

1841.29 cm^2 / 5 students = 368.258 cm^2 (This is the variance)

Step 5: Take the square root of the variance Finally, take the square root of the variance to get the standard deviation.

√368.258 cm = 19.19 cm

So, the standard deviation of the sample is 19.19 cm.