Question

1. A researcher has obtained the number of hours worked per week during the semester for a sample of 10 students:

21, 33, 26, 16, 32, 20, 29, 20, 19, 20

Use the data set to compute the mean, the median, the mode, the range, the sample variance, the sample standard deviation, the 10th percentile, The sum of the squared deviations of each value of X from the mean. Briefly explain what information about the variable is provided by your answers for the mean, median, mode, and standard deviation.

Answer 1

Mean = Sum of terms / Number of terms

= 236 / 10

= 23.6

Median

the median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

16   19   20   20   20   21   26   29   32   33   

As you can see, we do not have just one middle number but we have a pair of middle numbers, so the median is the average of these two numbers:

Median = ( 20 + 21 ) / 2 = 20.5

Mode

The mode of a set of data is the value in the set that occurs most often.

Ordering the data from least to greatest, we get:

16   19   20   20   20   21   26   29   32   33   

We see that the mode is 20 .

Range

The range is the difference between the highest and lowest values in the data set.

Ordering the data from least to greatest, we get:

16   19   20   20   20   21   26   29   32   33   

The lowest value is 16.

The highest value is 33.

The range = 33 - 16 = 17.

sample variance

data	data-mean	(data - mean)2
21	-2.6	6.76
33	9.4	88.36
26	2.4	5.76
16	-7.6	57.76
32	8.4	70.56
20	-3.6	12.96
29	5.4	29.16
20	-3.6	12.96
19	-4.6	21.16
20	-3.6	12.96

from the above calculations