The following give the number of hours spent doing homework and attending classes by 10 randomly selected college students during the past one week.86172429-25321921Calculate median, mode, first quartile, third quartile and variance for these data

Sure, let's start by organizing the data in ascending order:

7, 9, 18, 21, 21, 24, 25, 29, 32, 86

1. Median: The median is the middle value of a data set. Since we have 10 data points, we take the average of the 5th and 6th values. So, (21+24)/2 = 22.5

2. Mode: The mode is the most frequently occurring value in a data set. In this case, the mode is 21 because it appears twice, more than any other value.

3. First Quartile (Q1): This is the median of the first half of the data. Since we have 10 data points, the first half is the first 5 numbers. The median of 7, 9, 18, 21, 21 is 18.

4. Third Quartile (Q3): This is the median of the second half of the data. The second half of our data is the last 5 numbers. The median of 24, 25, 29, 32, 86 is 29.

5. Variance: The variance is a measure of how spread out the numbers in the data set are. First, calculate the mean (average) of the data set. Then, subtract the mean from each number and square the result. Finally, average these squared results.

Mean = (7+9+18+21+21+24+25+29+32+86)/10 = 30.2

Then, calculate each deviation squared: (7-30.2)^2 = 537.64 (9-30.2)^2 = 448.36 (18-30.2)^2 = 148.84 (21-30.2)^2 = 84.64 (21-30.2)^2 = 84.64 (24-30.2)^2 = 38.44 (25-30.2)^2 = 27.04 (29-30.2)^2 = 1.44 (32-30.2)^2 = 3.24 (86-30.2)^2 = 3113.64

Sum of squared deviations = 4488.52

Variance = Sum of squared deviations / (Number of data points - 1) = 4488.52 / 9 = 498.724

So, the median is 22.5, the mode is 21, the first quartile is 18, the third quartile is 29, and the variance is approximately 498.724.