In a survey, several people were asked

toni.kiwoi

toni.kiwoi

Answered question

2022-05-04

In a survey, several people were asked how many years it has been since they purchased a mattress. The results are shown in the table.

Years since last purchase     0    1    2    3    4     5    
Number of people

3

9

16

22

17

9

 

Evaluate the following (Express the answer in 2 decimal places):

a) Standard deviation (4 Marks)

 

 

b) Coefficient of variation (1 Mark)

 

 

c) Expected value of x, that is E(x) (2 Marks)

 

 

d) Variance of x, that is Var(x)(3 Marks)

 

 

e) The probability of having bought a mattress in the last 3 years. (1 Mark) 

 

Answer & Explanation

Andre BalkonE

Andre BalkonE

Skilled2023-05-29Added 110 answers

To calculate the standard deviation of the given data, we can use the following formula:
Standard deviation=(xx¯)2n
where:
- x represents the number of years since the last mattress purchase,
- x¯ is the mean (average) of the data set,
- n is the total number of observations.
First, let's calculate the mean (x¯). We can do this by summing the products of each number of years and its corresponding frequency, and then dividing by the total number of people:
x¯=(x·frequency)frequency
Calculating the sum of the products of years and frequencies:
0·3+1·9+2·16+3·22+4·17+5·9=150
Calculating the sum of the frequencies:
3+9+16+22+17+9=76
Now, we can calculate the mean:
x¯=15076=1.97
Next, we need to calculate the sum of squared deviations from the mean. We subtract the mean from each number of years, square the result, and then multiply by the frequency:
(01.97)2·3+(11.97)2·9+(21.97)2·16+(31.97)2·22+(41.97)2·17+(51.97)2·9=76.72
Finally, we can calculate the standard deviation:
Standard deviation=76.72761.01
Therefore, the standard deviation of the data set is approximately 1.01 when expressed in 2 decimal places.

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