Question

I/ The following data are ACT test scores from a group of high school seniors: 30, 25, 29, 32, 27, 25, 24, 18, 26 1/ Find the mode 2/ Find the mean 3/ Construct a boxplot (clearly label all 5 specific values) 4/ Calculate the standard deviation for the data set

Answer 1

1. 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:

18   24   25   25   26   27   29   30   32   

We see that the mode is 25 .

2. Mean=

3. For box plot we will compute below

The minimum is the smallest value in a data set.

Ordering the data from least to greatest, we get:

18   24   25   25   26   27   29   30   32   

So, the minimum is 18.

The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.

18   24   25   25   26   27   29   30   32   

So, the bottom half is

18   24   25   25   

The median of these numbers is 24.5.

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:

18   24   25   25   26   27   29   30   32   

So, the median is 26 .

The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.

18   24   25   25   26   27   29   30   32   

So, the upper half is

27   29   30   32   

The median of these numbers is 29.5.

The maximum is the greatest value in a data set.

Ordering the data from least to greatest, we get:

18   24   25   25   26   27   29   30   32   

So, the maximum is 32.

So box plot is

4.

Create the following table.

data	data-mean	(data - mean)2
18	-8.2222	67.60457284
24	-2.2222	4.93817284
25	-1.2222	1.49377284
25	-1.2222	1.49377284
26	-0.2222	0.04937284
27	0.7778	0.60497284
29	2.7778	7.71617284
30	3.7778	14.27177284
32	5.7778	33.38297284

Find the sum of numbers in the last column to get.

Hence