Question

1. 20 18 23 30 20 12 23 9 15

a. find the mean, median, mode and range.

b. Find the standard deviation by hand. (complete the chart).

x x-x̅ (x-x̅)²

Answer 1

a. Mean value is

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:

9   12   15   18   20   20   23   23   30   

So, the median is 20 .

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:

9   12   15   18   20   20   23   23   30   

Since both 20 and 23 occur 2 times, the modes are 20 and 23 ( this data set is bimodal).

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

Ordering the data from least to greatest, we get:

9   12   15   18   20   20   23   23   30   

The lowest value is 9.

The highest value is 30.

The range = 30 - 9 = 21.

b. Create the following table.

data	data-mean	(data - mean)2
20	1.1111	1.23454321
18	-0.8889	0.79014321
23	4.1111	16.90114321
30	11.1111	123.45654321
20	1.1111	1.23454321
12	-6.8889	47.45694321
23	4.1111	16.90114321
9	-9.8889	97.79034321
15	-3.8889	15.12354321

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

Hence standard deviation is