Question

The following data are the temperatures of effluent at discharge from a sewage treatment facility on 24 randomly selected days: 42 46 50 48 52 50 46 49 45 52 46 51 44 49 46 51 49 45 44 50 48 50 49 50 Calculate the following: (a) sample mean: (b) sample median: (c) sample variance: (d) sample standard deviation: (e) first quartile (Q1): (f) third quartile (Q3)

Answer 1

Answer:

a) 48

b) 49

c) 7.3333

d) 2.708

e) 46

f) 50

Step-by-step explanation:

(a) sample mean

Add the data up and divide by the number of data (24)

We will get

Mean = 1152/24 = 48

(b) sample median

We need to order the data:

42 44 44 45 45 46 46 46 46 48 48 49 49 49 49 50 50 50 50 50 51 51 52 52  

Now you have 2 groups of 12 data each  

42 44 44 45 45 46 46 46 46 48 48 49

and  

49 49 49 50 50 50 50 50 51 51 52 52

and we can see there are 12 data to the left of 49 and 12 data to the right of 49, so 49 is the median

(c) sample variance

Subtract the mean=48 you just found in (a) from each number in the list and you 24 new values

-6 -4 -4 -3 -3 -2 -2 -2 -2 0 0 1 1 1 1 2 2 2 2 2 3 3 4 4  

 

square each value of the new list

36 16 16 9 9 4 4 4 4  0 0 1 1 1 1 4 4 4 4 4 9 9 16 16  

add the numbers up and divide by the number of data

Variance = 176/24 = 7.3333

(d) sample standard deviation

The standard deviation is the square root of the variance so

Standard Deviation = $\large\bf \sqrt{7.3333}=2.708$

(e) first quartile (Q1)

Q1 is the median of the first half of data we found in (b)

Q1 = 46 (there are ¼ of the data to the left of 46)

(f) third quartile (Q3)

Q3 is the median of the second half of data we found in (b)

Q3 = 50 (there are ¼ of the data to the right of 46)