The table shows the distribution of the number of hours per day spent in studying by 50 students. Number of hours per day 4 5 6 7 8 9 10 11 Number of studen...

Answer Details

To find the mean and standard deviation, we can use the following formulas:

Mean (average) = (sum of all values) / (total number of values)

Standard deviation = sqrt((sum of (value - mean)^2) / (total number of values))

Let's first find the mean:

Multiply the number of hours by the number of students in that category and add up the results for all categories:

(4 x 5) + (5 x 7) + (6 x 5) + (7 x 9) + (8 x 12) + (9 x 4) + (10 x 3) + (11 x 5) = 411

The total number of students is 50, so:

Mean (average) = 411 / 50 = 8.22 (correct to two decimal places)

Therefore, the mean number of hours per day spent in studying by these 50 students is 8.22.

Next, let's find the standard deviation:

First, find the difference between each value and the mean, square each difference, and then add up the results:

[(4 - 8.22)^2 x 5] + [(5 - 8.22)^2 x 7] + [(6 - 8.22)^2 x 5] + [(7 - 8.22)^2 x 9] + [(8 - 8.22)^2 x 12] + [(9 - 8.22)^2 x 4] + [(10 - 8.22)^2 x 3] + [(11 - 8.22)^2 x 5] = 201.2

Divide the sum by the total number of values and take the square root:

Standard deviation = sqrt(201.2 / 50) = 1.99 (correct to two decimal places)

Therefore, the standard deviation is 1.99.

In conclusion, the mean number of hours per day spent in studying by these 50 students is 8.22, and the standard deviation is 1.99.