Question

Given the following data below, compute the following statistics:

       15        25        24        15        20        30        25    

a)The median

b)The mode

c)The range and the midrange

d)?65_!"

e)The mean

f)The variance

g)The standard deviation

Answer 1

(a) Median

The median is the middle number in a sorted list of numbers.

Numbers in ascending order:

15   15   20   24   25   25   30   

So, the median is 24 .

(b) Mode

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

15   15   20   24   25   25   30   

Here 15 and 25 occur 2 times, the modes are 15 and 25 ( this data set is bimodal).

(c) The range and midrange

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

15   15   20   24   25   25   30   

Lowest value is 15.

Highest value is 30.

Range = 30 - 15 = 15.

Midrange = ( Max value + MIn value) /2 = 30 + 15 = 45/2 = 22.5

Midrange= 22.5

(d) P65

n=7

i=p / 100 * n= (65/ 100) * 7 = 4.55

i= 5 (rounding off to interger)

The percentile is at the position i = 5

Nos in asscending order: 15   15   20   24   25   25   30   

65th percentile = 25.

(e) Mean = sum of all terms / no of terms = 154 / 7 = 22

Mean = 22

f) variance

data	data-mean	(data - mean)2
15	-7	49
25	3	9
24	2	4
15	-7	49
20	-2	4
30	8	64
25	3	9

var = 31.3333

g) standard deviation

s = 5.5976