 Mathematics
13 January, 06:17

# Answer questions (a-e) for the following set of data. 3,9,10,5,8,5,9,11,10,3,10A) Find the mean of the data.B) Find the median of the data.C) Find the mode of the data.D) Find the range of the data,E) Find the standard deviation of the data

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1. 13 January, 07:49
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Step-by-step explanation:

The set of data is 3,9,10,5,8,5,9,11,10,3,10

Rearranging the data so that the smallest one comes first, it becomes

3,3,5,5,8,9,9,10,10,10,11

a) mean of the data = sum of the digits / total number of digits. It becomes

(3+3+5+5+8+9+9+10+10+10+11) / 11

= 83/11 = 7.545

b) median is the middle number. Therefore,

Median = 9

c) the mode of the data is the most occurring number in the data. Therefore,

Mode = 10 (it occurred three times)

d) the range of the data is the difference between the highest and the lowest number. The highest number is 11 and the lowest number is 3. Therefore,

Range = 11-3 = 8

e) standard deviation = √[ (summation (x-u) ^2]/n

Where u = mean = 7.545

(x-u) ^2 will become

(3-7.545) ^2 = 20.66

(3-7.545) ^2 = 20.66

(5-7.545) ^2 = 6.48

(5-7.545) ^2 = 6.48

(8-7.545) ^2 = 0.21

(9-7.545) ^2 = 2.12

(9-7.545) ^2 = 2.12

(10-7.545) ^2 = 6.03

(10-7.545) ^2 = 6.03

(10-7.545) ^2 = 6.03

(11-7.545) ^2 = 11.94

(summation (x-u) ^2) / n = 88.76/11=8.07

Standard deviation = √8.07 = 2.84